TY - JOUR

T1 - Extensions of G-Posets and Quillen'S Complex Yoav Segev and Peter Webb

AU - Segev, Yoav S.

N1 - Funding Information:
© 1994 Australian Mathematical Society 0263-6115/94 $A2.00 + 0.00 The second author was partially supported by the NSF.

PY - 1994/1/1

Y1 - 1994/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84972192091&partnerID=8YFLogxK

U2 - 10.1017/S1446788700036053

DO - 10.1017/S1446788700036053

M3 - Article

AN - SCOPUS:84972192091

VL - 57

SP - 60

EP - 75

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 1

ER -