Date of this Version
Published in ISRAEL JOURNAL OF MATHEMATICS 211 (2016), 311–347. DOI: 10.1007/s11856-015-1274-5
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 shortlex conjugacy language in virtually cyclic groups, proving one direction of a conjecture of Rivin.