The Addition theorem for two-step nilpotent torsion groups

TL;DR

This paper proves that the Addition Theorem for algebraic entropy, previously established for abelian and certain torsion groups, also holds for two-step nilpotent torsion groups, expanding its applicability.

Contribution

It extends the validity of the Addition Theorem for algebraic entropy to two-step nilpotent torsion groups, a class where it was previously unknown.

Findings

Addition Theorem holds for two-step nilpotent torsion groups

Extends previous results from abelian and quasihamiltonian groups

Shows failure of additivity in metabelian groups

Abstract

The Addition Theorem for the algebraic entropy of group endomorphisms of torsion abelian groups was proved in [4]. Later, this result was extended to all abelian groups [3] and, recently, to all torsion finitely quasihamiltonian groups [7]. In contrast, when it comes to metabelian groups, the additivity of the algebraic entropy fails [8]. Continuing the research within the class of locally finite groups, we prove that the Addition Theorem holds for two-step nilpotent torsion groups.