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Shlossberg, Menachem
Journal of group theory, 07/2023, Letnik: 26, Številka: 4Journal Article
The Addition Theorem for the algebraic entropy of group endomorphisms of torsion abelian groups was proved in D. Dikranjan, B. Goldsmith, L. Salce and P. Zanardo, Algebraic entropy for abelian groups, (2009), 7, 3401–3434. Later, this result was extended to all abelian groups D. Dikranjan and A. Giordano Bruno, Entropy on abelian groups, (2016), 612–653 and, recently, to all torsion finitely quasihamiltonian groups A. Giordano Bruno and F. Salizzoni, Additivity of the algebraic entropy for locally finite groups with permutable finite subgroups, (2020), 5, 831–846. In contrast, when it comes to metabelian groups, the additivity of the algebraic entropy fails A. Giordano Bruno and P. Spiga, Some properties of the growth and of the algebraic entropy of group endomorphisms, (2017), 4, 763–774. Continuing the research within the class of locally finite groups, we prove that the Addition Theorem holds for two-step nilpotent torsion groups.
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