On central topological groups

Abstract

1. Introduction. Let G be a locally compact topological group and Z(G) its center. We shall be concerned with the class [Z] of all locally compact groups G such that GZ(G) is compact. It turns out that the various structural results on groups in [Z] generalize and unify in a natural manner those of compact groups on the one hand, and of locally compact abelian groups on the other. The present paper gives complete proofs of the results announced in Bull. Amer. Math. Soc. 72 (1966), 831-836 under the same title. 2 contains various elementary conditions for groups G to be in [Z] and [SIN] and is preparatory in character.