КОНЕЧНЫЕ ГРУППЫ C ЗАДАННЫМИ СИСТЕМАМИ \(tcc_n\)-ПОДГРУПП
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Abstract
The subgroups \(A\) and \(B\) are said to be \(\text{cc}\)-permutable, if \(A\) permutes with \(B^g\) for some \(g \in \langle A, B \rangle\). A subgroup \(A\) of a finite group \(G\) is called \(\text{tcc}_n\)-subgroup of \(G\), if there exists a subgroup \(T\) of \(G\) such that \(G = AT\) and every normal subgroup of \(A\) is \(\text{cc}\)-permutable with all subgroups of \(T\). In this paper we proved the supersolubility of the group \(G\) factorized by supersoluble \(\text{tcc}_n\)-subgroups \(A\) and \(B\). In addition, we obtained the supersolubility of a group whose maximal, Sylow, maximal of Sylow, minimal, 2-maximal subgroups are \(\text{tcc}_n\)-subgroups.
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