On the Theorem of Maschke

V. S. Charin

National Taras Shevchenko University of Kyiv

Abstract: 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 $A$.

UDC: 512.4

Received: 18.04.1968

 English version: Mathematical Notes, 1968, 4:2, 582–583

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