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degree of commutativity

Proceedings of the Edinburgh Mathematical Society (1)

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The Conjugacy Ratio of Groups
Part of
- Special aspects of infinite or finite groups
- Probabilistic methods in group theory
Laura Ciobanu, Charles Garnet Cox, Armando Martino
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 62 / Issue 3 / August 2019

Published online by Cambridge University Press:

22 February 2019, pp. 895-911
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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.