PUB - Publikationen an der Universität Bielefeld

In this paper we study the class [A] of all locally compact groups G with the property that for each closed subgroup H of G there exists a pair of homomorphisms into a compact group with H as coincidence set, and the class [D] of all locally compact group G with the property that finite dimensional unitary representations of subgroups of G can be extended to finite dimensional representations of G. It is shown that [MOORE]-groups (every irreducible unitary representation is finite dimensional) have these two properties. A solvable group in [D] is a [MOORE]-group. Moreover, we prove a structure theorem for Lie groups in the class [MOORE], and show that compactly generated Lie groups in [MOORE] have faithful finite dimensional unitary representations.