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 -divisible group, and let G be a compact totally disconnected -group of automorphisms of A, where 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.Translated from Matematicheskie Zametki, Vol. 4, No. 2, pp. 151–154, August, 1968.