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