On Quillen's conjecture for p-solvable groups

TL;DR

This paper offers new proofs of Quillen's conjecture for p-solvable groups, utilizing geometric methods and the Classification of Finite Simple Groups, including an asymptotic version without it.

Contribution

It introduces a novel geometric proof for Quillen's conjecture in p-solvable groups and presents an asymptotic version independent of the Classification of Finite Simple Groups.

Findings

New geometric proof of Quillen's conjecture for solvable groups

Asymptotic version of the conjecture without relying on CFSG

Verification of the conjecture for p-solvable groups

Abstract

We give a new proof of Quillen's conjecture for solvable groups via a geometric and explicit method. For p-solvable groups, we provide both a new proof using the Classification of Finite Simple Groups and an asymptotic version without employing it.