Authors: Yoav Segev, Peter Webb

home page: http://www.math.umn.edu/~webb

Address:
School of Mathematics,
University of Minnesota,
Minneapolis MN 55455

Title:
Extensions of G-posets and Quillen’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.