2004/05/31 by Alexander Fel’shtyn, Fel'shtyn, Alexander, Daciberg Lima Gonçalves +1 · 1 citation
Computer Science · Mathematics · #20E45 #37C25 #55M20 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0405590
openalex publication_date 2004/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let ϕ:G → G be a group endomorphism where G is a finitely generated group of exponential growth, and denote by R(ϕ) the number of twisted ϕ-conjugacy classes. Fel'shtyn and Hill \citefel-hill conjectured that if ϕ is injective, then R(ϕ) is infinite. This conjecture is true for automorphisms of non-elementary Gromov hyperbolic groups, see \citell and \cite fel:1. It was showed in \cite gw:2 that the conjecture does not hold in general. Nevertheless in this paper, we show that the conjecture holds for the Baumslag-Solitar groups B(m,n), where either |m| or |n| is greater than 1 and |m|≠ |n|. We also show that in the cases where |m|=|n|>1 or mn=-1 the conjecture is true for automorphisms. In addition, we derive few results about the coincidence Reidemeister number.