Authors: Yoav Segev, Peter Webb
email: webb@math.umn.edu
home page: http://www.math.umn.edu/~webb
Address:
School of Mathematics,
University of Minnesota,
Minneapolis MN 55455
Title:
Extensions of G-posets and Quillenâ€™s complex
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.
Subject Classification: Primary 20D30; Secondary 05E25, 06A09, 20C20, 51E25.
Journal: J. Australian Math. Soc. (Series A) 57 (1994), 60-75.