Baer--Suzuki theorem for the $\pi$-radical

TL;DR

This paper extends the Baer-Suzuki theorem to the context of the $ ext{pi}$-radical in finite groups, assuming the classification of finite simple groups, providing new insights into the structure of these radicals.

Contribution

It proves an analogue of the Baer-Suzuki theorem for the $ ext{pi}$-radical in finite groups, contingent on the classification of finite simple groups.

Findings

Established the $ ext{pi}$-radical analogue of Baer-Suzuki theorem

Dependent on the classification of finite simple groups

Enhances understanding of the structure of $ ext{pi}$-radicals

Abstract

In the paper we prove (modulo the classification of finite simple groups) an analogue of the famous Baer-Suzuki theorem for the $\pi$-radical of a finite group, where $\pi$ is a set of primes