An OD-Characterizable Class of Simple Groups

TL;DR

This paper proves that certain finite simple groups with a maximum prime divisor of 37 are uniquely identified by their order and degree pattern among all finite groups.

Contribution

It introduces a new characterization of finite simple groups with prime divisors up to 37 based on order and degree pattern.

Findings

Finite simple groups with max prime 37 are OD-characterizable.

Unique determination by order and degree pattern for these groups.

Extends understanding of group identification methods.

Abstract

It is proved that finite nonabelian simple groups $S$ with $\max \pi(S)=37$ are uniquely determined by their order and degree pattern in the class of all finite groups.