On the sharp Baer--Suzuki theorem for $\pi$-radicals: sporadic groups

Nanying Yang; Zhenfeng Wu; Danila O. Revin

doi:10.1134/S0037446622020161

On the sharp Baer--Suzuki theorem for $\pi$-radicals: sporadic groups

Group Theory 2023-01-02 v1

Authors: Nanying Yang , Zhenfeng Wu , Danila O. Revin

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Abstract

Let $\pi$ be a proper subset of the set of all primes. Denote by $r$ the smallest prime which does not belong to $\pi$ and set $m = r$ if $r = 2$ or $3$ and $m = r-1$ if $r \geqslant 5$ . We study the following conjecture: a conjugacy class $D$ of a finite group $G$ is contained in the $\pi$ -radical $\mathrm{O}_\pi(G)$ of $G$ if and only if every $m$ elements of $D$ generate a $\pi$ -subgroup. We confirm this conjecture for each group $G$ whose nonabelian composition factors are isomorphic to sporadic or alternating groups.

Keywords

baer-suzuki theorem pi-radical finite groups conjugacy class sporadic groups alternating groups pi-subgroup

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@article{arxiv.2111.09066,
  title  = {On the sharp Baer--Suzuki theorem for $\pi$-radicals: sporadic groups},
  author = {Nanying Yang and Zhenfeng Wu and Danila O. Revin},
  journal= {arXiv preprint arXiv:2111.09066},
  year   = {2023}
}

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On the sharp Baer--Suzuki theorem for $\pi$-radicals: sporadic groups

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