Control of fusion by elementary abelian subgroups of rank at least 2

TL;DR

This paper proves that elementary abelian subgroups of rank at least 2 can control p-fusion for odd primes, improving existing theorems in the field.

Contribution

It extends the control of p-fusion to a broader class of subgroups, specifically elementary abelian of rank ≥ 2, for odd primes.

Findings

Elementary abelian subgroups of rank ≥ 2 control p-fusion for odd primes

Improvement of Theorem B from previous work for odd primes

Enhanced understanding of subgroup control in p-fusion theory

Abstract

In this paper, we focus on the subgroups control $p$-fusion, and we improve the Theorem B of [4] for odd prime. For odd prime, we prove that elementary abelian subgroups of rank at least 2 can control $p$-fusion(see our Theorem B).