On fixed point sets and Lefschetz modules for sporadic simple groups |
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Authors: | John Maginnis |
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Affiliation: | Mathematics Department, Kansas State University, 137 Cardwell Hall, Manhattan, KS 66506, United States |
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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 p3, 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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Keywords: | Primary, 20C20, 20C34 secondary, 05E25 |
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