Degree of commutativity of infinite groups

Antolín, Yago; Martino, Armando; Ventura, Enric

doi:10.1090/proc/13231

Degree of commutativity of infinite groups
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by Yago Antolín, Armando Martino and Enric Ventura PDF

Proc. Amer. Math. Soc. 145 (2017), 479-485 Request permission

Abstract:

We prove that, in a finitely generated residually finite group of subexponential growth, the proportion of commuting pairs is positive if and only if the group is virtually abelian. In particular, this covers the case where the group has polynomial growth (i.e., virtually nilpotent groups). We also show that for non-elementary hyperbolic groups, the proportion of commuting pairs is always zero.

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