Beltran, A., Jose Felipe, M., Melchor, C. (2018). Conjugacy classes contained in normal subgroups: an overview. International Journal of Group Theory, 7(1), 23-36. doi: 10.22108/ijgt.2017.21216

Antonio Beltran; Maria Jose Felipe; Carmen Melchor. "Conjugacy classes contained in normal subgroups: an overview". International Journal of Group Theory, 7, 1, 2018, 23-36. doi: 10.22108/ijgt.2017.21216

Beltran, A., Jose Felipe, M., Melchor, C. (2018). 'Conjugacy classes contained in normal subgroups: an overview', International Journal of Group Theory, 7(1), pp. 23-36. doi: 10.22108/ijgt.2017.21216

Beltran, A., Jose Felipe, M., Melchor, C. Conjugacy classes contained in normal subgroups: an overview. International Journal of Group Theory, 2018; 7(1): 23-36. doi: 10.22108/ijgt.2017.21216

Conjugacy classes contained in normal subgroups: an overview

^{2}Universitat Politécnica de València

Abstract

We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework of graphs associated to the conjugacy classes, which have been introduced and developed in the past few years. We will see how the properties of these graphs, along with some extensions of the classic Landau's Theorem on conjugacy classes for normal subgroups, have been used in order to classify groups and normal subgroups satisfying certain conjugacy class numerical conditions.

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