A characterization of PSL(2,q), q = 5,7

TL;DR

This paper proves that the groups PSL(2,5) and PSL(2,7) are uniquely identified by the structure of their subgroup class posets, challenging a previous conjecture about such characterizations.

Contribution

It demonstrates that PSL(2,5) and PSL(2,7) are characterized by their subgroup class posets, providing a counterexample to an existing conjecture.

Findings

PSL(2,5) and PSL(2,7) are uniquely determined by their subgroup posets

Disproves the conjecture that these groups are not characterized by their subgroup class structures

Establishes a new understanding of subgroup poset characterizations for certain simple groups

Abstract

In this short note we prove that the finite non-abelian simple groups PSL(2,q), where q = 5,7, are determined by their posets of classes of isomorphic subgroups. In particular, this disproves the conjecture in the end of [5].