Conjugacy classes contained in normal subgroups: an overview

Document Type : Ischia Group Theory 2016

Authors

1 Universitat Jaume I

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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References

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International Journal of Group Theory
Volume 7, Issue 1 - Serial Number 1
Proceedings of the Ischia Group Theory 2016-Part I
March 2018
Pages 23-36

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History

  • Receive Date: 13 October 2016
  • Revise Date: 13 February 2017
  • Accept Date: 17 January 2017
  • Published Online: 01 March 2018

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