The Addition Theorem for two-step nilpotent torsion groups
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Menachem Shlossberg
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 Theory 23 (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 Theory 20 (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.
Acknowledgements
It is a pleasure to thank the referee for the useful suggestions. In particular, for simplifying the proof of Proposition 5.1 using [3, Proposition 5.1.10].
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Communicated by: Benjamin Klopsch
References
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Articles in the same Issue
- Frontmatter
- Curvature distribution and hyperbolicity
- On Whitehead’s cut vertex lemma
- Abelian splittings and JSJ-decompositions of finitely presented Bestvina–Brady groups
- On endomorphisms of the direct product of two free groups
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- A note on torsion length and torsion subgroups
- On the separability of subgroups of nilpotent groups by root classes of groups
- The Addition Theorem for two-step nilpotent torsion groups
- A bound for the orders of centralizers of irreducible subgroups of algebraic groups
- The average character degree of finite groups and Gluck’s conjecture
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Articles in the same Issue
- Frontmatter
- Curvature distribution and hyperbolicity
- On Whitehead’s cut vertex lemma
- Abelian splittings and JSJ-decompositions of finitely presented Bestvina–Brady groups
- On endomorphisms of the direct product of two free groups
-
The
- A note on torsion length and torsion subgroups
- On the separability of subgroups of nilpotent groups by root classes of groups
- The Addition Theorem for two-step nilpotent torsion groups
- A bound for the orders of centralizers of irreducible subgroups of algebraic groups
- The average character degree of finite groups and Gluck’s conjecture
- Character degrees of normally monomial 𝑝-groups of maximal class
- Finite groups with an affine map of large order
- Classification of non-solvable groups whose power graph is a cograph
