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Ballester-Bolinches, A.; Beidleman, J. C.; Ragland, M. F.

Some characterisations of soluble SST-groups. (English) Zbl 1346.20019

Commun. Algebra 44, No. 4, 1821-1827 (2016).
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.
Reviewer: Enrico Jabara (Venezia)

Cited in 1 Document

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 permutability
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References:

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