Conjugacy languages in groups
Laura Ciobanu, Susan Hermiller, Derek Holt, and Sarah Rees
Keywords conjugacy problem, geodesics, formal languages
Status 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.
\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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