The degree of commutativity and lamplighter groups

被引：3
|
作者：
Cox, Charles Garnet [1 ]
机构：
[1] Univ Southampton, Math Sci, Southampton SO17 1BJ, Hants, England
来源：
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2018年 / 28卷 / 07期
关键词：
Wreath products; lamplighter group; degree of commutativity; exponential growth; FINITELY GENERATED GROUPS; TRANSLATION NUMBERS; CONJUGACY GROWTH;
D O I：
10.1142/S0218196718500510
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The degree of commutativity of a group G measures the probability of choosing two elements in G which commute. There are many results studying this for finite groups. In [Y. Antolin, A. Martino and E. Ventura, Degree of commutativity of infinite groups, Proc. Amer. Math. Soc. 145 (2017) 479-485, MR 3577854], this was generalized to infinite groups. In this note, we compute the degree of commutativity for wreath products of the form Z (sic) Z and F (sic) Z, where F is any finite group.
引用
收藏
页码：1163 / 1173
页数：11
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