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Adolfo Ballester-Bolinches, Luis M. Ezquerro, A. A. Heliel, and M. M. Al-Shomrani

Some results on products of finite groups

Bull. Malays. Math. Sci. Soc., 40(3):1341–1351, 2017

https://doi.org/10.1007/s40840-015-0111-7

Abstract

Subgroups A and B of a finite group are said to be mutually permutable (respectively, M-permutable and sn-permutable) if A permutes with every subgroup (respectively, every maximal subgroup and every subnormal subgroup) of B and viceversa. If every subgroup of A permutes with every subgroup of B, then the product is said to be totally permutable. These kinds of products have received much attention in the last twenty years. The aim of this paper is to analyse the behaviour of finite pairwise mutually permutable, mutually M-permutable, mutually sn-permutable and totally permutable products with respect to certain classes of groups including the supersoluble groups, widely supersoluble groups, and also the classes of PST-, PT– and T-groups.

2010 Mathematics Subject Classification: 20D10, 20D20, 20D40

Keywords: Finite group, Permutability, Products of groups,  Supersoluble group