# Limit points in the range of the commuting probability function on finite groups Journal article, 2013

If G is a finite group, then Pr(G) denotes the fraction of ordered pairs of elements of G which commute. We show that, if l \in (2/9,1] is a limit point of the function Pr on finite groups, then l \in \Q and there exists an e = e_l > 0 such that Pr(G) \not\in (l - e_l, l) for any finite group G. These results lend support to some old conjectures of Keith Joseph.

## Author

#### Peter Hegarty

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

#### Journal of Group Theory

1433-5883 (ISSN)

Vol. 16 2 235-247

#### Subject Categories

Algebra and Logic

Basic sciences

#### DOI

10.1515/jgt-2012-0040

10/8/2017