We study the growth of group endomorphisms, a generalization of the classical notion of growth of finitely generated groups, which is strictly related to algebraic entropy. We prove that the inner automorphisms of a group have the same growth type and the same algebraic entropy as the identity automorphism. Moreover, we show that endomorphisms of locally finite groups cannot have intermediate growth.We also find an example showing that the Addition Theorem for algebraic entropy does not hold for endomorphisms of arbitrary groups.

Giordano Bruno, A., Spiga, P. (2017). Some properties of the growth and of the algebraic entropy of group endomorphisms. JOURNAL OF GROUP THEORY, 20(4), 763-774 [10.1515/jgth-2016-0050].

Some properties of the growth and of the algebraic entropy of group endomorphisms

Spiga, P
2017

Abstract

We study the growth of group endomorphisms, a generalization of the classical notion of growth of finitely generated groups, which is strictly related to algebraic entropy. We prove that the inner automorphisms of a group have the same growth type and the same algebraic entropy as the identity automorphism. Moreover, we show that endomorphisms of locally finite groups cannot have intermediate growth.We also find an example showing that the Addition Theorem for algebraic entropy does not hold for endomorphisms of arbitrary groups.
Articolo in rivista - Articolo scientifico
Algebra and Number Theory
English
2017
20
4
763
774
none
Giordano Bruno, A., Spiga, P. (2017). Some properties of the growth and of the algebraic entropy of group endomorphisms. JOURNAL OF GROUP THEORY, 20(4), 763-774 [10.1515/jgth-2016-0050].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/189779
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