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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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