Growth rate for endomorphisms of finitely generated nilpotent groups and solvable groups

2014/11/24 by Alexander Fel’shtyn, Alexander Fel'shtyn, Fel'shtyn, Alexander +4
Computer Science · Mathematics · #20F16 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Primary 20F65 #Secondary 20F18 #math.DS #math.GR #msc:20F16 #msc:20F18 #msc:20F65 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1411.6360

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openalex publication_date 2014/11/24 · arxiv created 2014/11/27 · arxiv updated 2014/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the growth rate of an endomorphism of a finitely generated nilpotent group equals to the growth rate of induced endomorphism on its abelinization, generalizing the corresponding result for an automorphism in [14]. We also study growth rates of endomorphisms for specific solvable groups, lattices of Sol, providing a counterexample to a known result in [5] and proving that the growth rate is an algebraic number.

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