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 PFMT, 2016, Issue 4(29), Pages 48–58 (Mi pfmt471)

MATHEMATICS

Finite groups with given generalized maximal subgroups (Review). I. Finite group with generalized normal $n$-maximal subgroup

V. A. Kovaleva

F. Scorina Gomel State University

Abstract: Let $G$ be a finite group. A chain of subgroups $H_n<H_{n-1}<…<H_1<H_0=G$ of $G$ such that $H_i$ is a maximal subgroup of $H_{i-1}$ for every $i=1,…,n$ is called a maximal chain of length $n$. A subgroup $H$ of $G$ is said to be an $n$-maximal subgroup of $G$ if $H$ is the latest member of some maximal chain of $G$ of length $n$. In this review, we give the analisis of the most famous papers in which finite groups with generalized normal $n$-maximal subgroups are developed.

Keywords: finite group, maximal subgroup, maximal chain, $n$-maximal subgroup, normal subgroup, subnormal subgroup, $K$-$\mathfrak{F}$-subnormal subgroup, permutable subgroup.

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Citation: V. A. Kovaleva, “Finite groups with given generalized maximal subgroups (Review). I. Finite group with generalized normal $n$-maximal subgroup”, PFMT, 2016, no. 4(29), 48–58

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\Bibitem{Kov16} \by V.~A.~Kovaleva \paper Finite groups with given generalized maximal subgroups (Review). I. Finite group with generalized normal $n$-maximal subgroup \jour PFMT \yr 2016 \issue 4(29) \pages 48--58 \mathnet{http://mi.mathnet.ru/pfmt471} 

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This publication is cited in the following articles:
1. V. A. Kovaleva, “Konechnye gruppy s zadannymi obobschenno maksimalnymi podgruppami (obzor). II. Ot maksimalnykh tsepei k maksimalnym param”, PFMT, 2017, no. 2(31), 55–65
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