Conjugacy languages in groups

Abstract

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.

29 pages

Cited by in corpus (2)

• Finite generating sets of relatively hyperbolic groups and applications to geodesic languages
• The conjugacy growth of the soluble Baumslag-Solitar groups