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A. Ballester-Bolinches, John Cossey, R. Esteban-Romero
Graphs and classes of finite groups
Note Mat., 33 (1), 89-94 (2013)
Abstract. There are different ways to associate to a finite group a certain graph. An interesting question is to analyse the relations between the structure of the group, given in group-theoretical terms, and the structure of the graph, given in the language of graph theory. This survey paper presents some contributions to this research line.
Keywords: finite groups, classes of groups, graphs
MSC 2000 classification: primary 20D10, secondary 05C25
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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