Una nota sui gruppi policiclici che ammettono un automorfismo con numero di Reidemeister finito |
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Authors: | Enrico Jabara |
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Affiliation: | (1) Dipartimento di Matematica Applicata, Universitá di Ca’ Foscari, Dorsoduro 3825/e, 30123 Venezia |
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Abstract: | LetG be a group and ϕ an automorphism ofG. Two elementsx, y ∈ G are called ϕ-conjugate if there existsg ∈ G such thatx=g −1 yg θ. It is easily verified that the ϕ-conjugation is an equivalence relation; the numberR(ϕ) of ϕ-classes ofG is called the Reidemeister number of the automorphism ϕ. In this paper we prove that if a polycyclic groupsG admits an automorphism ϕ of ordern such thatR(ϕ)<∞, thenG contains a subgroup of finite index with derived length at most 2 n−1 . |
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Keywords: | KeywordHeading" >MSC 2000 20F19 20E36 |
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