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Extensions of G-posets and Quillen's complex

Part of: Representation theory of groups Finite geometry and special incidence structures

Published online by Cambridge University Press:  09 April 2009

Yoav Segev  and
Peter Webb
Yoav Segev
Affiliation:
Department of Mathematics, Ben-Gurion Univesity, Beer-Sheva 84105, Israel
Peter Webb
Affiliation:
Department of Mathematics, University of MinnesotaMinneapolis, Minnesota 55455, USA
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Abstract

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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.

MSC classification

Secondary: 20D30: Series and lattices of subgroups 20C20: Modular representations and characters 51E25: Other finite nonlinear geometries
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 1 , August 1994 , pp. 60 - 75
Copyright
Copyright © Australian Mathematical Society 1994

References

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