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Conjugacy languages in groups

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arxiv 1401.7203 v1 pith:A23U6QBV submitted 2014-01-28 math.GR

Laura Ciobanu , Susan Hermiller , Derek Holt , Sarah Rees This is my paper · ORCID
classification math.GR
keywords conjugacygroupslanguagesvirtuallyabelianartinclassesconjecture
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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.

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  1. The conjugacy growth of the soluble Baumslag-Solitar groups

    math.GR 2019-08 accept novelty 7.0 of 10

    For each k at least 2, the conjugacy growth series of BS(1,k) with respect to the standard generating set is transcendental, and its growth rate equals the standard growth rate.

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