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Journal Article

Growth rate for endomorphisms of finitely generated nilpotent groups

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Fel'shtyn,  Alexander
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1515/jgth-2020-0097
(Publisher version)

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Citation

Fel'shtyn, A., Jo, J. H., & Lee, J. B. (2020). Growth rate for endomorphisms of finitely generated nilpotent groups. Journal of Group Theory, 23(6), 945-964. doi:10.1515/jgth-2020-0097.


Cite as: https://hdl.handle.net/21.11116/0000-0006-F062-C
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.