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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Conjugacy growth series and languages in groups


Authors: Laura Ciobanu and Susan Hermiller
Journal: Trans. Amer. Math. Soc. 366 (2014), 2803-2825
MSC (2010): Primary 20F65, 20E45
Published electronically: November 6, 2013
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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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Additional Information

Laura Ciobanu
Affiliation: Department of Mathematics, University of Neuchâtel, Rue Emile-Argand 11, CH-2000 Neuchâtel, Switzerland
Email: laura.ciobanu@unine.ch

Susan Hermiller
Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588-0130
Email: smh@math.unl.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-06052-7
PII: S 0002-9947(2013)06052-7
Keywords: Conjugacy growth, generating functions, graph products, regular languages
Received by editor(s): May 21, 2012
Received by editor(s) in revised form: October 30, 2012
Published electronically: November 6, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.