Homotopy equivalences between p-subgroup categories

TY - JOUR

T1 - Homotopy equivalences between p-subgroup categories

AU - Gelvin, Matthew Justin Karcher

AU - Møller, Jesper Michael

PY - 2015/7/1

Y1 - 2015/7/1

N2 - Let SG* be the Brown poset of nonidentity p-subgroups of the finite group G ordered by inclusion. Results of Bouc and Quillen show that SG* is homotopy equivalent to its subposets SG*+rad of nonidentity radical p-subgroups and SG*+eab of nonidentity elementary abelian p-subgroups. In this note we extend these results for the Brown poset of G to other categories of p-subgroups of G, including the p-fusion system of G.

AB - Let SG* be the Brown poset of nonidentity p-subgroups of the finite group G ordered by inclusion. Results of Bouc and Quillen show that SG* is homotopy equivalent to its subposets SG*+rad of nonidentity radical p-subgroups and SG*+eab of nonidentity elementary abelian p-subgroups. In this note we extend these results for the Brown poset of G to other categories of p-subgroups of G, including the p-fusion system of G.

U2 - 10.1016/j.jpaa.2014.10.002

DO - 10.1016/j.jpaa.2014.10.002

M3 - Journal article

SN - 0022-4049

VL - 219

SP - 3030

EP - 3052

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 7

ER -