The Conjugacy Ratio of Groups

Laura Ciobanu Radomirovic, Charles Garnet Cox, Armando Martino

Research output: Contribution to journalArticle

1 Citation (Scopus)
9 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)895-911
Number of pages17
JournalProceedings of the Edinburgh Mathematical Society
Volume62
Issue number3
Early online date22 Feb 2019
DOIs
Publication statusPublished - Aug 2019

Keywords

  • RAAGs
  • conjugacy growth
  • degree of commutativity
  • hyperbolic groups
  • polynomial growth
  • wreath products

ASJC Scopus subject areas

  • Mathematics(all)

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