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.
Milnor-Wolf Theorem for group endomorphisms
Giordano Bruno A.;
2020-01-01
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.File in questo prodotto:
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MWTh-iris.pdf
Open Access dal 16/03/2022
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