Algebraic entropy on topologically quasihamiltonian groups

TL;DR

This paper investigates algebraic entropy in topologically quasihamiltonian groups, offering a limit-free formula for calculation and establishing addition theorems, especially for quasihamiltonian torsion FC-groups.

Contribution

It introduces a limit-free formula for algebraic entropy and proves addition theorems in the context of topologically quasihamiltonian groups, including Hamiltonian groups.

Findings

Derived a limit-free formula for algebraic entropy.

Proved addition theorems for endomorphisms of quasihamiltonian groups.

Established the validity of the addition theorem for Hamiltonian groups.

Abstract

We study the algebraic entropy of continuous endomorphisms of compactly covered, locally compact, topologically quasihamiltonian groups. We provide a Limit-free formula which helps us to simplify the computations of this entropy. Moreover, several Addition Theorems are given. In particular, we prove that the Addition Theorem holds for endomorphisms of quasihamiltonian torsion FC-groups (e.g., Hamiltonian groups).