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M. J. Felipe, A. Martínez Pastor, and V. M. Ortiz-Sotomayor
Square-free class sizes in products of groups
J. Algebra, 491:190–206, 2017
We obtain some structural properties of a factorised group G=AB, given that the conjugacy class sizes of certain elements in A∪B are not divisible by p², for some prime p. The case when G=AB is a mutually permutable product is especially considered.
2010 Mathematical Subject Classification: 20D10, 20D40, 20E45
Keywords: Finite groups, Soluble groups, Products of subgroups, Conjugacy classes
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A. Ballester-Bolinches, John Cossey, Yangming Li
Mutually permutable products and conjugacy classes
Abstract: The question of how certain arithmetical conditions on the lengths of the conjugacy classes of a finite group G influence the group structure has been studied by several authors with many results available. The purpose of this paper is to analyse the restrictions imposed by the lengths of the conjugacy classes of some elements of the factors of a finite group G = G 1G2 · · · Gr , which is the product of the pairwise mutually permutable subgroups G 1, G 2, . . . , Gr , on its structure. Some earlier results appear as corollaries of our main theorems.
Keywords: Finite groups, Mutually permutable products, Conjugacy classes.
Mathematics Subject Classification: 20D10, 20D20, 20D40, 20E45