DEGREE OF COMMUTATIVITY OF INFINITE GROUPS

作者：Antolin Yago^*; Martino Armando; Ventura Enric

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145(2): 479-485.

DOI：10.1090/proc/13231

• Abelian groups
• degree of commutativity
• polynomial growth

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.

• 出版日期2017-2