Commuting Probability of Finite Groups (Extended)

Abstract

The target of this article is to discuss the concept of \textit{commuting probability} of finite groups which, in short, is a probabilistic measure of how abelian our group is. We shall compute the value of commuting probability for many special classes of non-abelian groups and also establish some local and global bounds. We will conclude with a few topics for further reading.

18 pages, expository, extended version of an article which appeared in Resonance, Indian Academy of Science