Conjugacy growth series and languages in groups

Ciobanu, Laura; Hermiller, Susan

doi:10.1090/S0002-9947-2013-06052-7

Conjugacy growth series and languages in groups
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by Laura Ciobanu and Susan Hermiller PDF

Trans. Amer. Math. Soc. 366 (2014), 2803-2825 Request permission

Abstract:

In this paper we introduce the geodesic conjugacy language and geodesic conjugacy growth series for a finitely generated group. We study the effects of various group constructions on rationality of both the geodesic conjugacy growth series and spherical conjugacy growth series, as well as on regularity of the geodesic conjugacy language and spherical conjugacy language. In particular, we show that regularity of the geodesic conjugacy language is preserved by the graph product construction, and rationality of the geodesic conjugacy growth series is preserved by both direct and free products.

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