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PFMT, 2019, Issue 1(38), Pages 61–64 (Mi pfmt624)  

MATHEMATICS

On the solvability of a finite group with a pair of non-conjugate subgroups of primary indices II

V. S. Monakhov, D. A. Khadanovich

F. Scorina Gomel State University

Abstract: The solvability of a finite group $G$ with two non-conjugate maximal subgroups $A$ and $B$ that satisfy the following requirements has been proved: subgroups $A$ and $B$ have primary indices in $G$; all proper subgroups of $A$ and $B$ are $2$-nilpotent. In addition, if $G$ is $S_4$-free and the indices of the subgroups $A$ and $B$ are coprime, then the $2$-nilpotency of the subgroups $A$ and $B$ can be replaced by their solvability.

Keywords: finite group, solvable group, maximal subgroup, $2$-nilpotent subgroup, non-conjugate subgroups, primary index.

Full text: PDF file (326 kB)
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UDC: 512.542
Received: 27.12.2018

Citation: V. S. Monakhov, D. A. Khadanovich, “On the solvability of a finite group with a pair of non-conjugate subgroups of primary indices II”, PFMT, 2019, no. 1(38), 61–64

Citation in format AMSBIB
\Bibitem{MonHod19}
\by V.~S.~Monakhov, D.~A.~Khadanovich
\paper On the solvability of a finite group with a pair of non-conjugate subgroups of primary indices~II
\jour PFMT
\yr 2019
\issue 1(38)
\pages 61--64
\mathnet{http://mi.mathnet.ru/pfmt624}


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