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