Skip to main content

Finite primitive permutation groups: A survey

  • Surveys
  • Conference paper
  • First Online:
Groups—Canberra 1989

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1456))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aschbacher, M., ‘On the maximal subgroups of the finite classical groups’, Invent. Math. 76 (1984), 469–514.

    Article  MathSciNet  MATH  Google Scholar 

  2. Aschbacher, M., ‘Maximal subgroups of finite alternating and symmetric groups’ (unpublished manuscript, 1985).

    Google Scholar 

  3. Aschbacher, M., and Scott, L., ‘Maximal subgroups of finite groups’, J. Algebra 92 (1985), 44–80.

    Article  MathSciNet  MATH  Google Scholar 

  4. Atkinson, M. D., ‘An algorithm for finding the blocks of a permutation group’, Math. Comp. 29 (1975), 911–913.

    Article  MathSciNet  MATH  Google Scholar 

  5. Babai, L., Luks, E. M., and Seress, A., ‘Permutation groups in NC’, in Proc. 19th ACM Symposium on Theory of Computing, to appear.

    Google Scholar 

  6. Babai, L., Luks, E. M., and Seress, A., ‘On managing permutation groups in O(n 4 log c n)’, Proc. 28th IEEE FOCS (1988), 272–282.

    Google Scholar 

  7. Baer, R., ‘Classes of finite groups and their properties’, Illinois J. Math. 1 (1957), 115–187.

    MathSciNet  MATH  Google Scholar 

  8. Bannai, E., ‘Maximal subgroups of low rank of finite symmetric and alternating groups’, J. Fac. Sci. Univ. Tokyo 18 (1972), 475–486.

    MathSciNet  MATH  Google Scholar 

  9. Biggs, N., ‘Presentations for cubic graphs’, in Computational Group Theory, Proceedings, Durham, 1982; ed. by Michael D. Atkinson, pp. 57–63 (Academic Press, London, New York, 1984).

    Google Scholar 

  10. Biggs, N., and Hoare, M., ‘The sextet construction for cubic graphs’, Combinatorica 3 (1983), 153–165.

    Article  MathSciNet  MATH  Google Scholar 

  11. van Bon, J., and Cohen, A. M., ‘Prospective classification of distance-transitive graphs’, in Proceedings of the Combinatorics 1988 Conf., Ravello, pp. 1–9.

    Google Scholar 

  12. van Bon, J., and Cohen, A. M., ‘Linear groups and distance-transitive graphs’, European J. Combin. 10 (1989), 399–412.

    Article  MathSciNet  MATH  Google Scholar 

  13. Brouwer, A. E., Cohen, A. M., and Neumaier, A., Distance Regular Graphs (Springer-Verlag, Berlin, 1989).

    Book  MATH  Google Scholar 

  14. Buekenhout, F., Delandtsheer, A., Doyen, J., Kleidman, P. B., Liebeck, M. W., and Saxl, J., ‘Linear spaces with flag-transitive automorphism groups’, Geom. Dedicata (to appear).

    Google Scholar 

  15. Burnside, W., Theory of Groups of Finite Order (Cambridge Univ. Press, Cambridge, 1911).

    MATH  Google Scholar 

  16. Butler, G., ‘Computing in permutation and matrix groups II; backtrack algorithm’, Math. Comp. 39 (1982), 671–680.

    MathSciNet  MATH  Google Scholar 

  17. Butler, G., ‘Computing normalizers in permutation groups’, J. Algorithms 4 (1983), 163–175.

    Article  MathSciNet  MATH  Google Scholar 

  18. Butler, G., and Cannon, J. J., ‘Computing in permutation and matrix groups I: normal closure, commutator subgroups, series’, Math. Comp. 39 (1982), 663–670.

    MathSciNet  MATH  Google Scholar 

  19. Butler, G., and Cannon, J. J., ‘Computing in permutation and matrix groups III: Sylow subgroups’, J. Symbolic Comput. 8 (1989), 241–252.

    Article  MathSciNet  MATH  Google Scholar 

  20. Cameron, P. J., ‘Permutation groups with multiply transitive suborbits, I’, Proc. London Math. Soc. (3) 25 (1972), 427–440.

    Article  MathSciNet  MATH  Google Scholar 

  21. Cameron, P. J., ‘Suborbits in transitive permutation groups’, in Combinatorics, Part 3: Combinatorial group theory, ed. by M. Hall Jr and J. H. van Lint, Math. Centre Tracts 57, pp. 98–129 (Math. Centrum, Amsterdam, 1974).

    Google Scholar 

  22. Cameron, P. J., ‘Finite permutation groups and finite simple groups’, Bull. London Math. Soc. 13 (1981), 1–22.

    Article  MathSciNet  MATH  Google Scholar 

  23. Cameron, P. J., and Cannon, J. J., ‘Recognizing doubly transitive groups’ (preprint, 1985).

    Google Scholar 

  24. Cameron, P. J., and Cannon, J. J., ‘Fast recognition of alternating and symmetric groups’ (preprint, 1986).

    Google Scholar 

  25. Cameron, P. J., Neumann, P. M., and Teague, D. N., ‘On the degrees of primitive permutation groups’, Math. Z. 180 (1982), 141–149.

    Article  MathSciNet  MATH  Google Scholar 

  26. Cameron, P. J., Praeger, C. E., Saxl, J., and Seitz, G. M., ‘On the Sims conjecture and distance transitive graphs’, Bull. London Math. Soc. 15 (1983), 499–506.

    Article  MathSciNet  MATH  Google Scholar 

  27. Cameron, P. J., and Praeger, C. E., ‘Graphs and permutation groups with projective subconstituents’, J. London Math. Soc. (2) 25 (1982), 62–74.

    Article  MathSciNet  MATH  Google Scholar 

  28. Cameron, P. J., and Praeger, C. E., ‘On 2-arc transitive graphs of girth 4’, J. Combin. Theory Ser. B 35 (1983), 1–11.

    Article  MathSciNet  MATH  Google Scholar 

  29. Cameron, P. J., and Praeger, C. E., ‘Block-transitive designs, I: point-imprimitive designs’, Discrete Math. (submitted).

    Google Scholar 

  30. Cameron, P. J., and Praeger, C. E., in preparation.

    Google Scholar 

  31. Cannon, J. J., ‘A computational toolkit for finite permutation groups’, in Proceedings of the Rutgers Group Theory Year 1983–1984, ed. by M. Aschbacher et al., pp. 1–18 (Cambridge University Press, New York, 1984).

    Google Scholar 

  32. Conder, M., ‘An infinite family of 5-arc transitive cubic graphs’, Ars Combinatoria 25A (1988), 95–108.

    MathSciNet  MATH  Google Scholar 

  33. Conder, M., ‘An infinite family of 4-arc transitive cubic graphs each with girth 12’, Bull. London Math. Soc. 21 (1989), 375–380.

    Article  MathSciNet  MATH  Google Scholar 

  34. Conder, M., and Lorimer, P., ‘Automorphism groups of symmetric graphs of valency 3’, J. Combin. Theory Ser. B 47 (1989), 60–72.

    Article  MathSciNet  MATH  Google Scholar 

  35. Cooperman, G., and Finkelstein, L. A., ‘A strong generating test and short presentations for permutation groups’, J. Symbolic Comput. (to appear).

    Google Scholar 

  36. Cooperman, G., Finkelstein, L., and Purdom, P. W., ‘Fast group membership using a strong generating test for permutation groups’, Proc. Computers and Math. (to appear).

    Google Scholar 

  37. Curtis, C. W., Kantor, W. M., and Seitz, G., ‘The 2-transitive permutation representations of the finite Chevalley groups’, Trans. Amer. Math. Soc. 218 (1976), 1–57.

    MathSciNet  MATH  Google Scholar 

  38. Cuypers, H., Geometries and permutation groups of small rank (Rijksuniversiteit, Utrecht, 1989).

    Google Scholar 

  39. Delandtsheer, A., ‘Line-primitive automorphism groups of finite linear spaces’, European J. Combin. 10 (1989), 161–169.

    Article  MathSciNet  Google Scholar 

  40. Delandtsheer, A., and Doyen, J., ‘Most block transitive t-designs are point primitive’, Geom. Dedicata 29 (1989), 397–410.

    Article  MathSciNet  MATH  Google Scholar 

  41. Dixon, J. D., and Mortimer, B., ‘The primitive permutation groups of degree less than 1000’, Math. Proc. Cam. Phil. Soc. 103 (1988), 213–238.

    Article  MathSciNet  MATH  Google Scholar 

  42. Djoković, D. Ž., and Miller, G. L., ‘Regular groups of automorphisms of cubic graphs’, J. Combin. Theory Ser. B 29 (1980), 195–230.

    Article  MathSciNet  Google Scholar 

  43. Faradzev, I. A., and Ivanov, A. A., ‘Distance-transitive representations of the groups G, PSL2(q)⩽G⩽PΓL2(q)’ (preprint, 1987).

    Google Scholar 

  44. Fein, B., Kantor, W. M., and Schacher, M., ‘Relative Brauer groups, II’, J. Reine Angew. Math. 328 (1981), 39–57.

    MathSciNet  MATH  Google Scholar 

  45. Fein, B., and Schacher, M., ‘Relative Brauer groups, I’, J. Reine Angew. Math. 321 (1981), 179–194.

    MathSciNet  MATH  Google Scholar 

  46. Fein, B., and Schacher, M., ‘Relative Brauer groups, III’, J. Reine Angew. Math. 335 (1982), 37–39.

    MathSciNet  MATH  Google Scholar 

  47. Förster, P., ‘On primitive groups with regular normal subgroups’ (preprint, 1985).

    Google Scholar 

  48. Förster, P., and Kovács, L. G., ‘On primitive groups with a single nonabelian regular normal subgroup’ (preprint, 1989).

    Google Scholar 

  49. Gardiner, A., ‘Symmetry conditions in graphs’, in Surveys in Combinatorics, ed. by B. Bollobás, London Math. Soc. Lecture Note Ser. 38, pp. 22–43 (Cambridge University Press, Cambridge, 1979).

    Chapter  Google Scholar 

  50. Goldschmidt, D. M., ‘Automorphisms of trivalent graphs’, Ann. of Math. 111 (1980), 377–406.

    Article  MathSciNet  MATH  Google Scholar 

  51. Guralnick, R. M., ‘Zeros of permutation characters with applications to prime splitting and Brauer groups’ (preprint, 1988).

    Google Scholar 

  52. Hering, C., ‘Transitive linear groups and linear groups which contain irreducible subgroups of prime order’, Geom. Dedicata 2 (1974), 425–460.

    Article  MathSciNet  MATH  Google Scholar 

  53. Hering, C., ‘Transitive linear groups and linear groups which contain irreducible subgroups of prime order, II’, J. Algebra 93 (1985), 151–164.

    Article  MathSciNet  MATH  Google Scholar 

  54. Hering, C., Liebeck, M. W., and Saxl, J., ‘The factorizations of the finite exceptional groups of Lie type’, J. Algebra 106 (1987), 517–527.

    Article  MathSciNet  MATH  Google Scholar 

  55. Higman, D. G., ‘Finite permutation groups of rank 3’, Math. Z. 86 (1964), 145–156.

    Article  MathSciNet  MATH  Google Scholar 

  56. Higman, D. G., ‘Primitive rank 3 groups with a prime subdegree’, Math. Z. 91 (1966), 70–86.

    Article  MathSciNet  MATH  Google Scholar 

  57. Higman, D. G., ‘Intersection matrices for finite permutation groups’, J. Algebra 6 (1967), 22–42.

    Article  MathSciNet  MATH  Google Scholar 

  58. Higman, D. G., and Sims, C. C., ‘A simple group of order 44,352,000’, Math. Z. 105 (1968), 110–113.

    Article  MathSciNet  MATH  Google Scholar 

  59. Holt, D. F., ‘The computation of normalizers in permutation groups’, J. Symbolic Comput. (to appear).

    Google Scholar 

  60. Hughes, D. R., and Piper, F. C., Design Theory (Cambridge University Press, Cambridge, 1985).

    Book  MATH  Google Scholar 

  61. Huppert, B., ‘Zweifach transitive, auflösbare Permutationsgruppen’, Math. Z. 68 (1957), 126–150.

    Article  MathSciNet  MATH  Google Scholar 

  62. Ivanov, A. A., ‘Distance-transitive graphs and their classification’ (preprint, 1989).

    Google Scholar 

  63. Jehne, W., ‘Kronecker classes of atomic extensions’, Proc. London Math. Soc. (3) 34 (1977), 32–64.

    Article  MathSciNet  MATH  Google Scholar 

  64. Jehne, W., ‘Kronecker classes of algebraic number fields’, J. Number Theory 9 (1977), 279–320.

    Article  MathSciNet  MATH  Google Scholar 

  65. Jerrum, M., ‘A compact representation for permutation groups’, J. Algorithms 7 (1986), 60–78.

    Article  MathSciNet  MATH  Google Scholar 

  66. Jones, G. A., and Soomro, K. D., ‘The maximality of certain wreath products in alternating and symmetric groups’, Quart. J. Math. Oxford (2) 37 (1986), 419–435.

    Article  MathSciNet  MATH  Google Scholar 

  67. Kantor, W. M., ‘Permutation representations of the finite classical groups of small degree or rank’, J. Algebra 60 (1979), 158–168.

    Article  MathSciNet  MATH  Google Scholar 

  68. Kantor, W. M., ‘Some consequences of the classification of finite simple groups’, in Finite groups—coming of age, ed. by John McKay, Contemporary Math. 45, pp. 159–173 (Amer. Math. Soc., Providence, 1985).

    Chapter  Google Scholar 

  69. Kantor, W. M., ‘Homogeneous designs and geometric lattices’, J. Combin. Theory Ser. A 38 (1985), 66–74.

    Article  MathSciNet  MATH  Google Scholar 

  70. Kantor, W. M., ‘Polynomial-time algorithms for finding elements of prime order and Sylow subgroups’, J. Algorithms 6 (1985), 478–514.

    Article  MathSciNet  MATH  Google Scholar 

  71. Kantor, W. M., ‘Sylow’s theorem in polynomial time’, J. Comput. System Sci. 30 (1985), 359–394.

    Article  MathSciNet  MATH  Google Scholar 

  72. Kantor, W. M., ‘Primitive permutation groups of odd degree, and an application to finite projective planes’, J. Algebra 106 (1987), 15–45.

    Article  MathSciNet  MATH  Google Scholar 

  73. Kantor, W. M., ‘Algorithms for computing in permutation groups’ (preprint, 1988).

    Google Scholar 

  74. Kantor, W. M., ‘Algorithms for Sylow p-subgroups and solvable groups’, in Computers in Algebra, pp. 77–90 (Marcel Dekker, New York, 1988).

    Google Scholar 

  75. Kantor, W. M., ‘Finding composition factors of permutation groups of degree n⩽106’, J. Symbolic Comput. (to appear).

    Google Scholar 

  76. Kantor, W. M., Liebeck, M. W., and Macpherson, H. D., ‘ℵ0-categorical structures smoothly approximated by finite substructures’ (preprint, 1988).

    Google Scholar 

  77. Kantor, W. M., and Liebler, R. A., ‘The rank 3 permutation representations of the finite classical groups’, Trans. Amer. Math. Soc. 71 (1982), 1–71.

    MathSciNet  MATH  Google Scholar 

  78. Kantor, W. M., and Taylor, D. E., ‘Polynomial-time versions of Sylow’s theorem’, J. Algorithms (to appear).

    Google Scholar 

  79. Klingen, N., ‘Zahlkörper mit gleicher Primzerlegung’, J. Reine Angew. Math. 299/300 (1978), 342–384.

    MathSciNet  MATH  Google Scholar 

  80. Klingen, N., ‘Atomare Kronecker-Klassen mit speziellen Galoisgruppen’, Abhandl. Math. Sem. Hamburg 48 (1979), 42–53.

    Article  MathSciNet  MATH  Google Scholar 

  81. Klingen, N., ‘Rigidity of decomposition laws and number fields’, J. Austral. Math. Soc. Ser. A (to appear).

    Google Scholar 

  82. Knapp, W., Über einige Fragen aus der Theorie der endlichen Permutationsgruppen, die sich in Zusammenhang mit einer Vermutung von Sims stellen (Habilitationsschrift, Universität Tübingen, 1977).

    Google Scholar 

  83. Kovács, L. G., ‘Maximal subgroups in composite finite groups’, J. Algebra 99 (1986), 114–131.

    Article  MathSciNet  MATH  Google Scholar 

  84. Kovács, L. G., ‘Primitive permutation groups of simple diagonal type’, Israel J. Math. 63 (1988), 119–127.

    Article  MathSciNet  MATH  Google Scholar 

  85. Kovács, L. G., ‘Primitive subgroups of wreath products in product action’, Proc. London Math. Soc. (3) 58 (1989), 306–322.

    Article  MathSciNet  MATH  Google Scholar 

  86. Kovács, L. G., ‘Twisted wreath products as primitive permutation groups’ (in preparation).

    Google Scholar 

  87. Lafuente, J., ‘Grupos primitivos con subgrupos maximales penquenos’, Publ. Sec. Mat. Univ. Auton. Barcelona 29 (1985), 154–161.

    MathSciNet  Google Scholar 

  88. Leedham-Green, C. R., Praeger, C. E., and Soicher, L. H., ‘Algorithms for finding the kernel of a group homomorphism’, J. Symbolic Comput. (to appear).

    Google Scholar 

  89. Leon, J. S., ‘On an algorithm for finding a base and strong generating set for a group given by generating permutations’, Math. Comp. 35 (1980), 941–974.

    Article  MathSciNet  MATH  Google Scholar 

  90. Liebeck, M. W., ‘The affine permutation groups of rank 3’, Proc. London Math. Soc. (3) 54 (1987), 477–516.

    Article  MathSciNet  MATH  Google Scholar 

  91. Liebeck, M. W., Praeger, C. E., and Saxl, J., ‘A classification of the maximal subgroups of the finite alternating and symmetric groups’, J. Algebra 111 (1987), 365–383.

    Article  MathSciNet  MATH  Google Scholar 

  92. Liebeck, M. W., Praeger, C. E., and Saxl, J., ‘On maximal subgroups and maximal factorizations of almost simple groups’, Proc. Symp. Pure Math. 47 (1987), 449–454.

    Article  MathSciNet  MATH  Google Scholar 

  93. Liebeck, M. W., Praeger, C. E., and Saxl, J., ‘On the O’Nan-Scott Theorem for finite primitive permutation groups’, J. Austral. Math. Soc. Ser. A 44 (1988), 389–396.

    Article  MathSciNet  MATH  Google Scholar 

  94. Liebeck, M. W., Praeger, C. E., and Saxl, J., ‘On the 2-closures of primitive permutation groups’, J. London Math. Soc. (2) 37 (1988), 241–252.

    Article  MathSciNet  MATH  Google Scholar 

  95. Liebeck, M. W., Praeger, C. E., and Saxl, J., ‘The factorizations of the finite simple groups and their automorphism groups’, Memoirs Amer. Math. Soc. 432 (1990) (to appear).

    Google Scholar 

  96. Liebeck, M. W., Praeger, C. E., and Saxl, J., ‘Finite primitive permutation groups containing regular subgroups’ (in preparation).

    Google Scholar 

  97. Liebeck, M. W., and Saxl, J., ‘Some recent results on finite permutation groups’, in Proceedings of the Rutgers Group Theory Year 1983–1984, ed. by M. Aschbacher et al., pp. 53–61 (Cambridge University Press, New York, 1984).

    Google Scholar 

  98. Liebeck, M. W., and Saxl, J., ‘The primitive permutation groups of odd degree’, J. London Math. Soc. (2) 31 (1985), 250–264.

    Article  MathSciNet  MATH  Google Scholar 

  99. Liebeck, M. W., and Saxl, J., ‘The finite primitive permutation groups of rank three’, Bull. London Math. Soc. 18 (1986), 165–172.

    Article  MathSciNet  MATH  Google Scholar 

  100. Luks, E. M., ‘Parallel algorithms for permutation groups and graph isomorphism’, Proc. 27th IEEE FOCS (1986), 292–302.

    Google Scholar 

  101. Luks, E. M., ‘Computing the composition factors of a permutation group in polynomial time’, Combinatorica 7 (1987), 87–99.

    Article  MathSciNet  MATH  Google Scholar 

  102. Luks, E. M., and McKenzie, P., ‘Fast parallel computation with permutation groups’, Proc. 26th IEEE FOCS (1985), 505–514.

    Google Scholar 

  103. Maillet, E., ‘Sur les isomorphes holoédriques et transitifs des groupes symetriques ou alternés’, J. Math. Pures Appl. (5) 1 (1895), 5–34.

    MATH  Google Scholar 

  104. Mathieu, E., ‘Mémoire sur l’étude des fonctions de plusieurs quantités’, J. Math. Pures Appl. (2) 6 (1861), 241–323.

    MathSciNet  Google Scholar 

  105. Mortimer, B., ‘Permutation groups containing affine groups of the same degree’, J. London Math. Soc. 15 (1977), 445–455.

    Article  MathSciNet  MATH  Google Scholar 

  106. Neumann, P. M., ‘Some algorithms for computing with finite permutation groups’, in Groups—St Andrews 1985, ed. by C. M. Campbell and E. F. Robertson, London Math. Soc. Lecture Note Ser. 121, pp. 59–92 (Cambridge University Press, Cambridge, 1986).

    Google Scholar 

  107. Nickel, W., Niemeyer-Nickel, A. C., O’Keefe, C., Penttila, T., and Praeger, C. E., ‘The block-transitive, point-imprimitive 2-(729,8,1) designs’ (preprint, 1990).

    Google Scholar 

  108. Nickel, W., Niemeyer, A., and Schönert, M., GAP, getting started and reference manual (RWTH Aachen, 1988).

    Google Scholar 

  109. O’Keefe, C., Penttila, T., and Praeger, C. E., ‘On block-transitive, point-imprimitive designs’, Discrete Math. (submitted).

    Google Scholar 

  110. Praeger, C. E., ‘Finite simple groups and finite primitive permutation groups’, Bull. Austral. Math. Soc. 28 (1983), 355–366.

    Article  MathSciNet  MATH  Google Scholar 

  111. Praeger, C. E., ‘Symmetric graphs and the classification of the finite simple groups’, in Groups—Korea 1983, ed. by A. C. Kim and B. H. Neumann, Lecture Notes in Math. 1098, pp. 99–110 (Springer-Verlag, Berlin, 1984).

    Chapter  Google Scholar 

  112. Praeger, C. E., ‘Primitive permutation groups with doubly transitive subconstituents’, J. Austral. Math. Soc. Ser. A 45 (1988), 66–77.

    Article  MathSciNet  MATH  Google Scholar 

  113. Praeger, C. E., ‘Covering subgroups of groups and Kronecker classes of fields’, J. Algebra 118 (1988), 455–463.

    Article  MathSciNet  MATH  Google Scholar 

  114. Praeger, C. E., ‘The inclusion problem for finite primitive permutation groups’, Proc. London Math. Soc. (3) 60 (1990), 69–88.

    MathSciNet  MATH  Google Scholar 

  115. Praeger, C. E., ‘Highly arc-transitive digraphs’, European J. Combin. 10 (1989), 281–292.

    Article  MathSciNet  MATH  Google Scholar 

  116. Praeger, C. E., ‘Kronecker classes of field extensions of small degree’, J. Austral. Math. Soc. Ser. A (to appear).

    Google Scholar 

  117. Praeger, C. E., ‘On octic extensions and a problem in group theory’, in Group Theory, Proceedings of the Singapore Group Theory Conference held at the National University of Singapore, 1987; ed. by Kai Nah Cheng and Yu Kiang Leong, pp. 443–463 (de Gruyter, Berlin, New York, 1989).

    Google Scholar 

  118. Praeger, C. E., Saxl, J., and Yokoyama, K., ‘Distance transitive graphs and finite simple groups’, Proc. London Math. Soc. (3) 55 (1987), 1–21.

    Article  MathSciNet  MATH  Google Scholar 

  119. Saxl, J., ‘On a question of W. Jehne concerning covering subgroups of groups and Kronecker classes of fields’, J. London Math. Soc. (2) 38 (1988), 243–249.

    Article  MathSciNet  MATH  Google Scholar 

  120. Scott, L. L., ‘Representations in characteristic p’, in The Santa Cruz conference on finite groups, ed. by Bruce Cooperstein and Geoffrey Mason, Proc. Symposia in Pure Math. 37, pp. 318–331 (Amer. Math. Soc., Providence, 1980).

    Google Scholar 

  121. Seitz, G. M., ‘Small rank permutation representations of finite Chevalley groups’, J. Algebra 28 (1974), 508–517.

    Article  MathSciNet  MATH  Google Scholar 

  122. Sims, C. C., ‘Determining the conjugacy classes of a permutation group’, in Computers in Algebra and Number Theory, SIAM-AMS Proc. 4, pp. 191–195, 1970.

    Google Scholar 

  123. Sims, C. C., ‘Graphs and finite permutation groups’, Math. Z. 95 (1967), 76–86.

    Article  MathSciNet  MATH  Google Scholar 

  124. Sims, C. C., ‘Computational methods in the study of permutation groups’, in Computational Problems in Abstract Algebra, ed. by J. Leech, pp. 169–183 (Pergamon Press, New York, 1970).

    Chapter  Google Scholar 

  125. Sims, C. C., ‘Computation with permutation groups’, in Proc. Second Symp. Symbolic and Algebraic Manipulation (Assn. Computing Mach., New York, 1971).

    Google Scholar 

  126. Thompson, J. G., ‘Bounds for the orders of maximal subgroups’, J. Algebra 14 (1970), 135–138.

    Article  MathSciNet  MATH  Google Scholar 

  127. Tierlinck, L., ‘Non-trivial t-designs without repeated blocks exist for all t’, Discrete Math. 65 (1987), 301–311.

    Article  MathSciNet  Google Scholar 

  128. Tutte, W. T., ‘A family of cubical graphs’, Proc. Cambridge Philos. Soc. 43 (1947), 459–474.

    Article  MathSciNet  MATH  Google Scholar 

  129. Tutte, W. T., ‘On the symmetry of cubic graphs’, Canad. J. Math. 11 (1959), 621–624.

    Article  MathSciNet  MATH  Google Scholar 

  130. Weiss, R., ‘s-transitive graphs’, in Algebraic Methods in Graph Theory, Coll. Math. Soc. János Bolyai 25, pp. 827–847, 1984.

    Google Scholar 

  131. Weiss, R., ‘The non-existence of 8-arc transitive graphs’, Combinatorica 1 (1981), 309–311.

    Article  MathSciNet  MATH  Google Scholar 

  132. Weiss, R., ‘Distance-transitive graphs and generalised polygons’, Arch. Math. (Basel) 45 (1985), 186–192.

    Article  MathSciNet  MATH  Google Scholar 

  133. Wielandt, H., Finite Permutation Groups (Academic Press, New York, 1964).

    MATH  Google Scholar 

  134. Wielandt, H., Subnormal subgroups and permutation groups (Ohio State University, 1971).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

L. G. Kovács

Additional information

Dedicated to B.H. Neumann, my mentor and friend with love and good wishes for his eightieth birthday

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Praeger, C.E. (1990). Finite primitive permutation groups: A survey. In: Kovács, L.G. (eds) Groups—Canberra 1989. Lecture Notes in Mathematics, vol 1456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100731

Download citation

  • DOI: https://doi.org/10.1007/BFb0100731

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53475-4

  • Online ISBN: 978-3-540-46900-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics