On a class of supersoluble groups. (Q2922933)

In this paper so-called MS-groups are characterized. A group is, by definition, an MS-group if the maximal subgroups of all Sylow subgroups of \(G\) are \(S\)-semipermutable in \(G\). A subgroup \(H\) is said to be \(S\)-semipermutable in a group \(G\) if \(H\) permutes with every Sylow \(q\)-subgroup of \(G\) for all primes \(q\) not dividing the order of \(H\). Recall that a subgroup \(U\) of \(G\) is said to be permutable in \(G\) if \(UT=TU\) for all subgroups \(T\) of \(G\). Moreover, so-called \(T_0\)-groups are involved here; that is \(G\) is a \(T_0\)-group by definition if the Frattini factor group \(G/\Phi(G)\) is a \(T\)-group. A group \(G\) is by definition a \(T\)-group if normality is a transitive relation in \(G\).NEWLINENEWLINE As to explicit results in this paper, the reader is referred to it. Classification problems related, have been discussed by A. Ballester-Bolinches, R. Esteban-Romero, M. C. Pedraza-Aguilera, J. C. Beidleman, M. F. Ragland, Y. C. Ren, the reviewer and A. Fransman, L. and Y. Wang, Y. Li. -- For details, see the References in the paper.