Abstract
Leech [9] and Birkhoff and Hall [1] are standard references to computational group theory. The lesser-known Petrick [13] contains many articles on symbolic manipulation and group-theoretic work including a description by Sims of techniques he has developed to compute with very large degree permutation groups. These ideas have been used by him [14] most impressively to prove the existence and uniqueness of Lyons’ simple group of order 51 765 179 004 000 000 = 2837567.11.31.37.67 by constructing a permutation representation of it on the coasts of a subgroup G 2(5) of index 8 835 156. It should be added that Lyons’ group has no proper subgroup larger than G 2(5).
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References
Garrett Birkhoff and Marshall Hall, Jr., Computers in algebra and number theory, Proc. Sympos. Appl. Math. Amer. Math. Soc. and the Soc. Indust. Appl. Math., New York City, 1970, 4 (Amer. Math. Soc., Providence, RhodeIsland, 1971). Z61. 236. 00006.
Richard Brauer, “Representations of finite groups”, Lectures on Modern. Mathematics [Ed. T.L. Saaty], 1, pp. 133–175 (John Wiley & Sons, New York, London, 1963). MR31#2314.
J.H. Conway, “Three lectures on exceptional groups”, Finite simple groups [ed. M.B. Powell and G. Higman], pp. 215–247 (Academic Press, London and New York, 1971). Zb1. 221. 20014.
Larry Finkelstein, “The maximal subgroups of Conway’s group C3 and McLaughlin’s group”, J. Algebra 25 (1973), 58–89.
L. Finkelstein and A. Rudvalis, “Maximal subgroups of the Hall-Janko-Wales group”, J. Algebra 24 (1973), 486–493.
Dieter Held, “The simple groups related to M24 ”, J. Algebra 13 (1969), 253–296. MR40#2745.
G. Higman, “Construction of simple groups from character tables”, Finite simple groups [ed. M.B. Powell and G. Higman], 205–214 ( Academic Press, London and New York, 1971 ). Zb1.221.20014.
Graham Higman and John McKay, “On Janko’s simple group of order 50, 232, 960 ”, Bull. London Math. Soc. 1 (1969), 89–94; Correction: Bull. London Math. Soc. 1 (1969), 219. MR40#224.
John Leech (editor), Computational problems in abstract algebra (Oxford, 1967), (Pergamon Press, Oxford, 1970). MR4045374.
Richard Lyons, “Evidence for a new finite simple group”, J. Algebra 20 (1972), 540–569. MR45#8722.
John McKay, “Subgroups and permutation characters”, Computers in algebra and number theory [ed. Garrett Birkhoff and Marshall Hall, Sr.], Proc. Sympos. Appl. Math. Amer. Math. Soc. and the Soc. Indust. Appl. Math., New York City, 1970, 4, pp. 177–181 ( Amer. Math. Soc., Providence, Rhode Island, 1971 ).
Spyros S. Magliveras, “The subgroup structure of the Higman-Sims simple group”, Bull. Amer. Math. Soc. 77 (1971), 535–539. MR44#310.
Stanley Roy Petrick (editor), Second Symposium on symbolic and algebraic manipulation,Special Interest Group on Symbolic and Algebraic Manipulation Proceedings (Assoc. for Computing Machinery, 1971).
C.C. Sims, to appear.
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© 1974 Springer-Verlag Berlin Heidelberg
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McKay, J. (1974). Computing with Finite Simple Groups. In: Newman, M.F. (eds) Proceedings of the Second International Conference on the Theory of Groups. Lecture Notes in Mathematics, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21571-5_47
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DOI: https://doi.org/10.1007/978-3-662-21571-5_47
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