Algebraic entropy on strongly compactly covered groups

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 $\varphi :G\to G$ of these groups we compute the algebraic entropy and study its properties. Also an Addition Theorem is available under suitable conditions.