Algebraic entropy on strongly compactly covered groups

TL;DR

This paper introduces strongly compactly covered groups, a new class of locally compact groups, and studies the algebraic entropy of their continuous endomorphisms, including an addition theorem under certain conditions.

Contribution

It defines strongly compactly covered groups and computes algebraic entropy for their endomorphisms, extending entropy theory to this new class.

Findings

Computed algebraic entropy for strongly compactly covered groups.

Established an addition theorem for algebraic entropy in this context.

Characterized properties of these groups related to entropy.

Abstract

We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For continuous endomorphisms $\phi:G\to G$ of these groups we compute the algebraic entropy and study its properties. Also an Addition Theorem is available under suitable conditions.