Limit points in the range of the commuting probability function on finite groups

被引：7

作者：

Hegarty, Peter ^{[1
,2
]}

机构：

[1] Chalmers, Dept Math Sci, S-41296 Gothenburg, Sweden

[2] Univ Gothenburg, S-41296 Gothenburg, Sweden

来源：

JOURNAL OF GROUP THEORY | 2013年 / 16卷 / 02期

关键词：

CONJUGACY CLASSES; COMMUTATIVITY; ELEMENTS; NUMBER;

D O I：

10.1515/jgt-2012-0040

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 is an element of (2/9, 1] is a limit point of the function Pr on finite groups, then l is an element of Q and there exists an epsilon = epsilon(l) > 0 such that Pr(G) (sic) (l -epsilon(l), l) for any finite group G. These results lend support to some old conjectures of Keith Joseph.

引用

页码：235 / 247

页数：13