ON FINITE GROUPS IN WHICH SS-SEMIPERMUTABILITY IS A TRANSITIVE RELATION
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Abstract:
Let H be a subgroup of a finite group G. We say that H is SS-semipermutable in Gif H has a supplement K in G such that H permutes with every Sylow subgroup X of Kwith (jXj; jHj) = 1. In this paper, the Structure of SS-semipermutable subgroups, and finitegroups in which SS-semipermutability is a transitive relation are described. It is shown thata finite solvable group G is a PST-group if and only if whenever H K are two p-subgroupsof G, H is SS-semipermutable in NG(K).
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Journal title
volume 4 issue 1
pages 29- 36
publication date 2016-09-01
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