Author

Sheng-Min Zhang

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Preprint Oct 2026

Ordinary $G$-permutable subgroups of finite simple groups

We completely solve part (a) of Problem 17.112 in the Kourovka Notebook. We prove that a non-abelian finite simple group $G$ has a proper non-trivial ordinary $G$-permutable subgroup if and only if $G$ is isomorphic to ${\rm PSL_2(q)}$ where $q\geq4$ is a prime power and $q\not\equiv3\pmod4$, ${}^2B_2(2^{2a+1})$ where...

Sheng-Min Zhang · 1 citation · ⚡1

Preprint Oct 2026

A proof of the Galt--Tyutyanov conjecture on Skiba's question

A subgroup $A$ of a finite group $G$ is \emph{hereditarily $G$-permutable} if, for every subgroup $E$ with $A\leq E\leq G$ and every subgroup $B$ of $E$, some $G$-conjugate of $B$ permutes with $A$ in $E$. We give a new criterion for a finite group to be simple. A nontrivial finite group $G$ is simple if and only if it...

Sheng-Min Zhang · 0 citations