arXiv 2105.024422021-05-06math.GR

On the sharp Baer--Suzuki theorem for the $π$-radical

Nanying Yang, Zhenfeng Wu, Danila O. Revin, Evgeny P. Vdovin

备注：: in Russian
发表信息：: Mat. Sb., 214:1 (2023), 113-154
DOI：: 10.4213/sm9698

英文摘要：

Let $π$ be a set of primes such that $|π|\geqslant 2$ and $π$ differs from the set of all primes. Denote by $r$ the smallest prime which does not belong to $π$ and set $m=r$ if $r=2,3$ 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 $Oπ(G)$ if and only if every $m$ elements of $D$ generate a $π$-subgroup. We confirm this conjecture for each group $G$ whose nonabelian composition factors are isomorphic to alternating, linear and unitary simple groups.

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