Geodesic
Finite groups with $OS$-propermutable subgroups
Čebyševskij sbornik, Tome 22 (2021) no. 3, pp. 457-463.

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A subgroup $A$ of a group $G$ is called $OS$-propermutable in $G$ if there is a subgroup $B$ such that $G = N_G(A)B$, $AB$ is a subgroup of $G$ and the subgroup $A$ permutes with all Schmidt subgroups of $B$. In this situation, the subgroup $B$ is called $OS$-prosupplement to $A$ in $G$. In this paper, we proved the $p$-solubility of a finite group $G$ such that a Sylow $p$-subgroup of $G$ is $OS$-propermutable in $G$, where $p>5$.
Keywords: finite group, $p$-soluble group, $OS$-propermutable subgroup, Schmidt subgroup, seminormal subgroup. 
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E. V. Zubei. Finite groups with $OS$-propermutable subgroups. Čebyševskij sbornik, Tome 22 (2021) no. 3, pp. 457-463. http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a29/

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