On the Theorem of Maschke

It will be shown that the Theorem of Maschke can be carried over to certain classes of topological groups in the following way. Let $A$ be a locally compact abelian strictly $\Pi$-divisible group, and let $G$ be a compact totally disconnected $\Pi$-group of automorphisms of $A$, where $\Pi$ is a set of prime numbers. If a $G$-admissible subgroup $B$ of $A$ is isolated as a direct summand, then it has a $G$-admissible complement in $A$.