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- Title
The Addition Theorem for two-step nilpotent torsion groups.
- Authors
Shlossberg, Menachem
- Abstract
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, Trans. Amer. Math. Soc.361 (2009), 7, 3401–3434]. Later, this result was extended to all abelian groups [D. Dikranjan and A. Giordano Bruno, Entropy on abelian groups, Adv. Math.298 (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, J. Group Theory23 (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, J. Group Theory20 (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.
- Subjects
ABELIAN groups; FINITE groups; NILPOTENT groups; ENDOMORPHISMS; ENDOMORPHISM rings; TORSION; ENTROPY
- Publication
Journal of Group Theory, 2023, Vol 26, Issue 4, p779
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/jgth-2022-0060