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arXiv · 1709.02152

The conjugacy ratio of groups

Laura Ciobanu·Charles Garnet Cox·Armando Martino
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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.

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Laura Ciobanu, Charles Garnet Cox, Armando Martino. 2017-09-07. The conjugacy ratio of groups. https://doi.org/10.1017/s0013091518000573

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