Nilpotent $p$-local finite groups

TL;DR

This paper extends classical criteria for p-nilpotency from finite groups to fusion systems and p-local finite groups, providing new characterizations inspired by established results.

Contribution

It generalizes existing p-nilpotency criteria to the setting of fusion systems and p-local finite groups, broadening their applicability.

Findings

Provides new characterizations of p-nilpotency for fusion systems

Generalizes classical criteria by Atiyah, Frobenius, and others

Enhances understanding of p-local finite groups structure

Abstract

In this paper we prove characterizations of $p$-nilpotency for fusion systems and $p$-local finite groups that are inspired by results in the literature for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.