Extensions of G-posets and Quillen’s complex

Yoav Segev, Peter Webb

Research output: Contribution to journalArticlepeer-review


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. Let G be a finite group and p a prime. Let Ap(G) be the Quillen complex of G at the prime p. Ap(G) is the order complex of the poset ( = partially ordered set) of all non-trivia
Original languageEnglish GB
Pages (from-to)60
Number of pages75
JournalJournal of the Australian Mathematical Society
Issue number1
StatePublished - 3 Feb 2009


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