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A. Ballester-Bolinches, Yangming Li, Ning Su, and Zhuoqing Xie.

On π-S-permutable subgroups of finite groups.

 Mediterr. J. Math., 13(1):93–99, 2016

https://doi.org/10.1007/s00009-014-0479-x

Abstract

Let π be a set of primes. A subgroup H of a finite group G is said to be π-S-permutable in G if H permutes with every Sylow q-subgroup of G for all primes q ∈ π. The main aim of this paper is to establish structural results about the normal closure of π-S-permutable subgroups and p-subgroups permuting with all p′-subgroups for a single prime p. Our results stem from a recent article by Isaacs and subsequent discussions with the authors about it.

2010 Mathematics Subject Classification: Primary 20D10; Secondary 20D15, 20D20, 20D40

Keywords: Finite group, Permutability, S-permutability, S-semipermutability, Normal closure