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 PFMT, 2019, Issue 3(40), Pages 88–92 (Mi pfmt661)

MATHEMATICS

Finite groups with restrictions on two maximal subgroups

V. S. Monakhov, A. A. Trofimuk, E. V. Zubei

F. Scorina Gomel State University

Abstract: A subgroup $A$ of a group $G$ is called seminormal in $G$, if there exists a subgroup $B$ such that $G = AB$ and $AB_1$ is a proper subgroup of $G$ for every proper subgroup $B_1$ of $B$. We introduce the new concept that unites subnormality and seminormality. A subgroup $A$ of a group $G$ is called semisubnormal in $G$, if either $A$ is subnormal in $G$, or is seminormal in $G$. In this paper we proved the supersolubility of a group $G$ under the condition that all Sylow subgroups of two non-conjugate maximal subgroups of $G$ are semisubnormal in $G$. Also we obtained the nilpotency of the second derived subgroup $(G')'$ of a group $G$ under the condition that all maximal subgroups of two non-conjugate maximal subgroups are semisubnormal in $G$.

Keywords: supersoluble groups, semisubnormal subgroup, derived subgroup, Sylow subgroup, maximal subgroup.

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Citation: V. S. Monakhov, A. A. Trofimuk, E. V. Zubei, “Finite groups with restrictions on two maximal subgroups”, PFMT, 2019, no. 3(40), 88–92

Citation in format AMSBIB
\Bibitem{MonTroZub19} \by V.~S.~Monakhov, A.~A.~Trofimuk, E.~V.~Zubei \paper Finite groups with restrictions on two maximal subgroups \jour PFMT \yr 2019 \issue 3(40) \pages 88--92 \mathnet{http://mi.mathnet.ru/pfmt661}