Fusion systems on p-groups of sectional rank 3

TL;DR

This paper classifies saturated fusion systems on p-groups of sectional rank 3 for odd primes, especially those without non-trivial normal p-subgroups, providing a comprehensive understanding of their structure.

Contribution

It offers a complete classification of certain fusion systems on p-groups of sectional rank 3 for all odd primes p, focusing on those without non-trivial normal p-subgroups.

Findings

Classification achieved for p ≥ 5

Identified conditions for fusion systems without normal p-subgroups

Enhanced understanding of fusion systems on p-groups of sectional rank 3

Abstract

We study saturated fusion systems on $p$-groups having sectional rank $3$ for all odd primes $p$. For $p\geq 5$, we obtain a complete classification of the ones that do not have any non-trivial normal $p$-subgroups.