Limit points in the range of the commuting probability function on finite groups
Group Theory
2012-07-04 v1
Abstract
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.
Cite
@article{arxiv.1207.0760,
title = {Limit points in the range of the commuting probability function on finite groups},
author = {Peter Hegarty},
journal= {arXiv preprint arXiv:1207.0760},
year = {2012}
}
Comments
11 pages, no figures