The conjugacy ratio of groups

Abstract

In this paper we introduce and study the conjugacy ratio of a finitely generated group, which is the limit at infinity of the quotient of the conjugacy and standard growth functions. We conjecture that the conjugacy ratio is $0$ for all groups except the virtually abelian ones, and confirm this conjecture for certain residually finite groups of subexponential growth, hyperbolic groups, right-angled Artin groups, and the lamplighter group.

15 pages

References in corpus (1)

• Rational growth and degree of commutativity of graph products

Cited by in corpus (2)

• Commuting probabilities of infinite groups
• The Conjugacy Ratio of Abelian-by-Cyclic Groups