We study the growth of group endomorphisms and we prove an analogue of Chou's extension of Milnor-Wolf Theorem. Indeed, if G is an elementary amenable group and ϕ:G→G is an endomorphism, then ϕ has either polynomial or exponential growth. This result follows by studying the growth of automorphisms of finitely generated groups, where we prove some stronger results.
Giordano Bruno, A., Spiga, P. (2020). Milnor-Wolf Theorem for group endomorphisms. JOURNAL OF ALGEBRA, 546(15 March 2020), 85-118 [10.1016/j.jalgebra.2019.10.037].
Milnor-Wolf Theorem for group endomorphisms
Spiga P.
2020
Abstract
We study the growth of group endomorphisms and we prove an analogue of Chou's extension of Milnor-Wolf Theorem. Indeed, if G is an elementary amenable group and ϕ:G→G is an endomorphism, then ϕ has either polynomial or exponential growth. This result follows by studying the growth of automorphisms of finitely generated groups, where we prove some stronger results.
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