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A. Ballester-Bolinches, J. C. Beidleman, and M. F. Ragland.
Some characterisations of soluble SST-groups.
Comm. Algebra, 44(4):1821–1827, 2016.
All groups considered in this paper are 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. Following [6 Chen, X. Y., Guo, W. B. (2014). Finite groups in which SS-permutability is a transitive relation. Acta Math. Hungar. 143(2):466–479.], we call a group G an SST-group provided that SS-permutability is a transitive relation in G, that is, if A is an SS-permutable subgroup of B and B is an SS-permutable subgroup of G, then A is an SS-permutable subgroup of G. The main aim of this paper is to present several characterisations of soluble SST-groups.
2010 Mathematics Subject Classification: Primary 20D10; Secondary 20D15, 20D20
Keywords: BT-group, Finite group, Soluble PST-group, SST-group