Conjugacy languages in groups

Laura Ciobanu, Susan Hermiller, Derek Holt, and Sarah Rees


conjugacy problem, geodesics, formal languages


Submitted for publication.


We study the regularity of several languages derived from conjugacy classes in a finitely generated group $G$ for a variety of examples including word hyperbolic, virtually abelian, Artin, and Garside groups. We also determine the rationality of the growth series of the \wsphcl \ in virtually cyclic groups, proving one direction of a conjecture of Rivin. \bigskip \noindent 2010 Mathematics Subject Classification: 20F65, 20E45; 20F67, 20F36. \noindent Key words: Conjugacy growth, regular languages, word hyperbolic groups, Artin groups, Garside groups. \

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