Components in characteristic and Quillen's conjecture
arXiv:2607.27500
summary
The paper proves that if a finite group contains a component that is a simple Lie-type group in characteristic p and has no nontrivial normal p‑subgroup, then the Quillen poset at p has nonzero rational homology, ruling out such components in minimal counterexamples to Quillen's conjecture.
Abstract
The purpose of this paper is to show that, under mild inductive assumptions, if a group contains a component that is a simple group of Lie type in characteristic and , then the Quillen poset of at 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 , where the conjecture is still open.
17 pages
Topics & keywords
#simple groups#lie type#characteristic p#quillen poset#rational homology#finite groupscomponentsimple group of Lie typeO_p(G)Quillen conjecturerational homologyposet