Components in characteristic p and Quillen's conjecture

2026/07/29 by Kevin Ivan Piterman
Mathematics · #math.AT #math.GR #msc:55P10 #msc:20D30 #msc:20E42 #msc:20D06

paper · pdf

17 pages

arxiv created 2026/07/29 · arxiv updated 2026/07/31

Abstract

The purpose of this paper is to show that, under mild inductive assumptions, if a group G contains a component that is a simple group of Lie type in characteristic p and O_p(G) = 1, then the Quillen poset of G at p has nonzero rational homology. In particular, this shows that such components cannot arise in a minimal counterexample to Quillen's conjecture. This result is of particular interest at the prime p=2, where the conjecture is still open.

Citations

• Spherical p-group complexes arising from finite groups of Lie type
• Quillen's conjecture and unitary groups
• Some results on Quillen's Conjecture via equivalent-poset techniques
• An approach to Quillen's conjecture via centralizers of simple groups

Related

• Quillen's conjecture and unitary groups
• A geometric approach to Quillen's conjecture
• An approach to Quillen's conjecture via centralizers of simple groups
• Some results on Quillen's Conjecture via equivalent-poset techniques
• On Quillen's conjecture for p-solvable groups