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Subgroups of the Conway Groups; the Simple Groups of Higman-Sims, McLaughlin, Hall-Janko and Suzuki; Local Subgroups; Conjugacy Classes

  • Robert L. GriessJr.
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

We describe the involvement in CO 0 of the simple groups of Hall-Janko, Suzuki, McLaughlin and Higman-Sims. In addition, we determine conjugacy classes of elements of small order and the structure of several local subgroups (recall that a p-local subgroup, for a prime p, is the normalizer of a nonidentity p-subgroup, and a local subgroup is a p-local subgroup for some prime p). Appendix 10C contains Conway’s original table of triangle and other stabilizers, along with additional material. Our treatment of the conjugacy classes is original and our treatment of the above simple groups does involve some revision.

Keywords

Conjugacy Class Simple Group Maximal Subgroup Point Stabilizer Minimal Normal Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Robert L. GriessJr.
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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