A note on groups with finite dual spaces

Lawrence Wasson Baggett

Vol. 31 (1969), No. 3, 569–572

DOI: 10.2140/pjm.1969.31.569

Abstract

If a locally compact group has only a finite number of inequivalent irreducible unitary representations, then one is tempted to conjecture that it is a finite group. The conjecture is known to be true in certain special cases. We present here a proof in case the group satisfies the second axiom of countability.

Mathematical Subject Classification

Primary: 22.20

Milestones

Received: 7 March 1969

Published: 1 December 1969