Some characterisations of soluble SST-groups. (English) Zbl 1346.20019
All groups in this review are understood to be finite. A subgroup \(H\) of a group \(G\) is said to be SS-permutable (or SS-quasinormal) in \(G\) if \(H\) has a supplement \(K\) in \(G\) such that \(H\) permutes with every Sylow subgroup of \(K\). A group \(G\) is an SST-group provided that SS-permutability is a transitive relation in \(G\).
The main aim of this paper is to present several characterizations of soluble SST-groups.
The main aim of this paper is to present several characterizations of soluble SST-groups.
Reviewer: Enrico Jabara (Venezia)
MSC:
20D40 | Products of subgroups of abstract finite groups |
20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |
20D20 | Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure |
Keywords:
permutable subgroups; quasinormal subgroups; SS-permutability; soluble SST-groups; transitive permutabilityReferences:
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