THE INFLUENCE OF CONJUGACY CLASS SIZES ON THE STRUCTURE OF FINITE GROUPS: A SURVEY-Reference-Cited by-同舟云学术

THE INFLUENCE OF CONJUGACY CLASS SIZES ON THE STRUCTURE OF FINITE GROUPS: A SURVEY

Published:2011-12 Issue:04 Volume:04 Page:559-588
ISSN:1793-5571
Container-title:Asian-European Journal of Mathematics
language:en
Short-container-title:Asian-European J. Math.

Author:

Camina A. R.¹,Camina R. D.²

Affiliation:

1. School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK

2. Fitzwilliam College, Cambridge, CB3 0DG, UK

Abstract

The importance of conjugacy classes for the structure of finite groups was recognised very early in the study of groups. In this survey we consider the results from the many articles which have developed this topic and examined the influence of conjugacy class sizes or the number of conjugacy classes on the structure of finite groups. Whilst we begin by mentioning the early results of Sylow and Burnside, our major objective is to highlight the more recent work and present some interesting questions which we hope will inspire further research.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793557111000459

Reference142 articles.

1. FINITE GROUPS WITH TWO p-REGULAR CONJUGACY CLASS LENGTHS II

4. On groups with conjugacy classes of distinct sizes

5. Group elements of prime power index

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