The conjugacy class number k(G) - a different perspective

Deepak Gumber; Hemant Kalra

The conjugacy class number k(G) - a different perspective

Group Theory 2014-04-21 v1

Authors: Deepak Gumber , Hemant Kalra

Abstract

Let $G$ be a finite group. Let $k(G)$ denote the number of conjugacy classes of $G$ and let $m(G)$ denote the least positive integer $n$ such that the union of any $n$ distinct non-trivial conjugacy classes of $G$ together with the identity of $G$ is a subgroup of $G$ . We prove that $m(G)=k(G)-1$ for all $m(G)\ge 2$ .

Keywords

conjugacy classes in groups finite group theory additive combinatorics

Cite

@article{arxiv.1404.4835,
  title  = {The conjugacy class number k(G) - a different perspective},
  author = {Deepak Gumber and Hemant Kalra},
  journal= {arXiv preprint arXiv:1404.4835},
  year   = {2014}
}

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2 pages

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