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Milnor-Wolf theorem for group endomorphisms. (English) Zbl 07148868
Summary: 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 $$\phi : G \rightarrow G$$ is an endomorphism, then $$\phi$$ 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.

##### MSC:
 20-XX Group theory and generalizations 16-XX Associative rings and algebras
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##### References:
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