On fixed point sets and Lefschetz modules for sporadic simple groups

Details On fixed point sets and Lefschetz modules for sporadic simple groups On fixed point sets and Lefschetz modules for sporadic simple groups

2008-02-16

arxiv.org/abs/0802.2333v1

Journal of Pure and Applied Algebra 213 (2009) 901-912

Mathematics

Group Theory

22 pages

Scientific paper

10.1016/j.jpaa.2008.09.011

We consider 2-local geometries and other subgroup complexes for sporadic simple groups. For six groups, the fixed point set of a noncentral involution is shown to be equivariantly homotopy equivalent to a standard geometry for the component of the centralizer. For odd primes, fixed point sets are computed for sporadic groups having an extraspecial Sylow p-subgroup of order p^3, acting on the complex of those p-radical subgroups containing a p-central element in their centers. Vertices for summands of the associated reduced Lefschetz modules are described.

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