Homotopy equivalences between p-subgroup categories

2013/01/02 by Matthew Gelvin, Gelvin, Matthew, Jesper Møller +1
Mathematics · #05E15 (Primary) 20J15 (Secondary) #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.AT #math.CO #math.GR #msc:05E15 #msc:20J15

paper · pdf · doi:10.48550/arxiv.1301.0193

19 pages. Second version

arxiv created 2014/06/18 · arxiv updated 2014/06/19

Abstract

Let p be a prime number and G a finite group of order divisible by p. Quillen showed that the Brown poset of nonidentity p-subgroups of G is homotopy equivalent to its subposet of nonidentity elementary abelian subgroups. We show here that a similar statement holds for the fusion category of nonidentity p-subgroups of G. Other categories of p-subgroups of G are also considered.

Related

• The homotopy types of the posets of p-subgroups of a finite group
• Some results on Quillen's Conjecture via equivalent-poset techniques
• Coset complexes of p-subgroups in finite groups
• Acyclic 2-dimensional complexes and Quillen's conjecture
• Truncated Quillen coplexes of p-groups