Conjugacy classes and normal subgroups in finite groups

Abstract

This thesis is framed within the study that analyzes the influence of the conjugacy classes on the structure of finite groups. Over the last few decades this has been a flourishing and active line of research. The contents are divided into two parts. The first one consists of four chapters about graphs of conjugacy classes contained in a normal subgroup and their structural impact in such subgroup. Furthermore, as an application of the properties of these graphs, we present a generalized version of the well-known Landau's Theorem for such classes. The second part contains two chapters about the information that the product of conjugacy classes provides about the non-simplicity of the group and the normal structure and solvability of some groups associated to these classes.