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Application of computers to questions like those of Burnside

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Burnside Groups

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 806))

Abstract

Computers have been used in seeking answers to questions related to those about periodic groups asked by Burnside in his influential paper of 1902. A survey is given of results obtained with the aid of computers and a key program which manipulates presentations for groups of prime-power order is described.

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References

  • William A. Alford, George Havas and M.F. Newman (1975), "Groups of exponent four", Notices Amer. Math. Soc. 22, A.301.

    Google Scholar 

  • A.J. Bayes, J. Kautsky and J.W. Wamsley (1974), "Computation in nilpotent groups (application)", Proc. Second Internat. Conf. Theory of Groups (Canberra, 1973), pp. 82–89 (Lecture Notes in Mathematics, 372. Springer-Verlag, Berlin, Heidelberg, New York). MR50#7299; Zbl.288.20032; RZ [1975], 6A324.

    MATH  Google Scholar 

  • John J. Cannon, Lucien A. Dimino, George Havas and Jane M. Watson (1973), "Implementation and analysis of the Todd-Coxeter algorithm", Math. Comp. 27, 463–490. MR49#390; Zbl.314.20028; RZ [1974], 5A243.

    Article  MathSciNet  MATH  Google Scholar 

  • John Cannon (1974), "A general purpose group theory program", Proc. Second Internat. Conf. Theory of Groups (Canberra, 1973), pp. 204–217 (Lecture Notes in Mathematics, 372. Springer-Verlag, Berlin, Heidelberg, New York). MR50#7300.

    MATH  Google Scholar 

  • N.D. Gupta and M.F. Newman (1974), "The nilpotency class of finitely generated groups of exponent four", Proc. Second Internat. Conf. Theory of Groups (Canberra, 1973), pp. 330–332 (Lecture Notes in Mathematics, 372. Springer-Verlag, Berlin, Heidelberg, New York). MR50#4752; Zbl.291.20034; RZ [1975], 6A320.

    MATH  Google Scholar 

  • Marshall Hall, Jr. (1977), "Computers in group theory", Topics in group theory and computation (Proceedings of the Summer School, University College, Galway, 1973), pp. 1–37 (Academic Press [Harcourt Brace Jovanovich], London, New York, San Francisco). MR56#9809; Zbl.382.20002.

    Google Scholar 

  • George Havas (1974), "A Reidemeister-Schreier program", Proc. Second Internat. Conf. Theory of Groups (Canberra, 1973), pp. 347–356 (Lecture Notes in Mathematics, 372. Springer-Verlag, Berlin, Heidelberg, New York).

    MATH  Google Scholar 

  • George Havas (to appear), "Commutators in groups expressed as products of powers", Comm. Algebra.

    Google Scholar 

  • George Havas and Tim Nicholson (1976), "Collection", SYMSAC '76 (Proc. ACM Sympos. on Symbolic and Algebraic Computation, Yorktown Heights, New York, 1976), pp. 9–14 (Association for Computing Machinery, New York).

    Chapter  Google Scholar 

  • George Havas, G.E. Wall, and J.W. Wamsley (1974), "The two generator restricted Burnside group of exponent five", Bull. Austral. Math. Soc. 10, 459–470. MR51#3298; Zbl.277#20025; RZ [1975], 6A255.

    Article  MathSciNet  MATH  Google Scholar 

  • Graham Higman (1959), "Some remarks on varieties of groups", Quart. J. Math. Oxford Ser. (2) 10, 165–178. MR22#4756; Zbl.89,13; RZ [1961], 8A180.

    Article  MathSciNet  MATH  Google Scholar 

  • John Leech (1963–1967), "Coset enumeration on digital computers", Proc. Cambridge Philos. Soc. 59, 257–267. (Privately reprinted 1967.) MR26#4513; Zbl.117,269; RZ [1963], 12A176.

    Article  MathSciNet  MATH  Google Scholar 

  • I.D. Macdonald (1973), "Computer results on Burnside groups", Bull. Austral. Math. Soc. 9, 433–438. MR49#5165; Zbl.267#20011; RZ [1974], 10A201.

    Article  MathSciNet  MATH  Google Scholar 

  • I.D. Macdonald (1974), "A computer application to finite p-groups", J. Austral. Math. Soc. 17, 102–112. MR51#13028; Zbl.277.20024; RZ [1974], 11A228.

    Article  MathSciNet  MATH  Google Scholar 

  • Hanna Neumann (1967), Varieties of groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, 37. Springer-Verlag, Berlin, Heidelberg, New York). MR35#6734; Zbl.251#20001; RZ [1968], 3A194H.

    Book  MATH  Google Scholar 

  • M.F. Newman (1976), "Calculating presentations for certain kinds of quotient groups", SYMSAC '76 (Proc. ACM Sympos. on Symbolic and Algebraic Computation, Yorktown Heights, New York, 1976), pp. 2–8 (Association for Computing Machinery, New York). See also: Abstract, Sigsam Bull. 10, no. 3, 5.

    MATH  Google Scholar 

  • Ю.П. Размыслов [Ju.P. Razmyslov] (1978), "О проблеме Холла-Хигмвна" [On a problem of Hall-Higman], Izv. Akad. Nauk SSSR Ser. Mat. 42, 833–847. Zbl.394.20030; RZ [1979], 1A246.

    MathSciNet  Google Scholar 

  • David Shield (1977), "The class of a nilpotent wreath product", Bull. Austral. Math. Soc. 17, 53–89. MR56#3266; Zbl.396.20015; RZ [1978], 9A232.

    Article  MathSciNet  MATH  Google Scholar 

  • M.R. Vaughan-Lee (1979), "Derived lengths of Burnside groups of exponent 4", Quart. J. Math. Oxford (2) 30, 495–504.

    Article  MathSciNet  MATH  Google Scholar 

  • G.E. Wall (1974), "On the Lie ring of a group of prime exponent", Proc. Second Internat. Conf. Theory of Groups (Canberra, 1973), pp. 667–690 (Lecture Notes in Mathematics, 372. Springer-Verlag, Berlin, Heidelberg, New York). MR50#10098; Zbl.286.20050; RZ [1975], 7A389.

    Google Scholar 

  • J.W. Wamsley (1974), "Computation in nilpotent groups (theory)", Proc. Second Internat. Conf. Theory of Groups (Canberra, 1973), pp. 691–700 (Lecture Notes in Mathematics, 372. Springer-Verlag, Berlin, Heidelberg, New York). MR50#7350; Zbl.288.20031; RZ [1975], 6A323.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT, Australia

    George Havas & M. F. Newman

Authors
  1. George Havas
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  2. M. F. Newman
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Jens L. Mennicke

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© 1980 Springer-Verlag

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Havas, G., Newman, M.F. (1980). Application of computers to questions like those of Burnside. In: Mennicke, J.L. (eds) Burnside Groups. Lecture Notes in Mathematics, vol 806. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091271

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  • DOI: https://doi.org/10.1007/BFb0091271

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10006-5

  • Online ISBN: 978-3-540-38120-4

  • eBook Packages: Springer Book Archive

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