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File: odd4.dvi

Author 1: John Maginnis
Address: Mathematics Department, Kansas State University, 137 Cardwell
Hall, Manhattan, Kansas 66506

Author 2: Silvia Onofrei
Address: Mathematics Department, Kansas State University, 137 Cardwell
Hall, Manhattan, Kansas 66506

Title:
On fixed point sets and Lefschetz modules for sporadic simple groups

Abstract:
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.

Preprint, January 2008