Geodesic
Finite groups with given Schmidt subgroups
Problemy fiziki, matematiki i tehniki, no. 1 (2022), pp. 84-88.

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Throughout the article, all groups are finite and $G$ always denotes a finite group. A subgroup $H$ of the group $G$ is called $\mathfrak{U}_p$-normal in $G$ ($p$ is a prime) if every chief factor of the group $G$ between $H^G$ and $H_G$ is either cyclic or a $p'$-group. In this article, we prove that if each Schmidt subgroup of the group $G$ is either subnormal or $\mathfrak{U}_p$-normal in $G$, then the derived subgroup $G'$ of $G$ is $p$-nilpotent. Some well-known results are generalized.
Keywords: finite group, nilpotent group, subnormal subgroup, $\mathfrak{U}_p$-normal subgroup, Schmidt group. 
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V. M. Sel'kin; V. S. Zakrevskaya; N. S. Kosenok. Finite groups with given Schmidt subgroups. Problemy fiziki, matematiki i tehniki, no. 1 (2022), pp. 84-88. http://geodesic.mathdoc.fr/item/PFMT_2022_1_a12/

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