J Austral Math Soc Ser A 57 pp60--75, 1994.

Extensions of G-Posets and Quillen's Complex

Yoav Segev and Peter Webb

Abstract

We develop techniques to compute the homology of Quillen's complex of elementary abelian p-subgroups of a finite group in the case where the group has a normal subgroup of order divisible by p. The main result is a long exact sequence relating the homologies of these complexes for the whole group, the normal subgroup, and certain centralizer subgroups. The proof takes place at the level of partially-ordered sets. Notions of suspension and wedge product are considered in this context, which are analogous to the corresponding notions for topological spaces. We conclude with a formula for the generalized Steinberg module of a group with a normal subgroup, and give some examples.

1991 AMS Subject Classification: primary 20D30; secondary 05E25, 06A09, 20C20, 51E25

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Authors

Yoav Segev

Department of Mathematics, Ben - Gurion University, Beer - Sheva 84105, Israel.

Peter Webb

Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA.