On some semigroup compactifications
by
Mahmoud Filali
Department of Mathematical Sciences, University of Oulu, FIN 90570 Finland

The LUC-compactification UG of a locally compact group is a semigroup with an operation which extends that of G and which is continuous (only) in one variable. When G is discrete, UG and the Stone-Cech compactification \betaG are identical. Some algebraic properties, such as the number of left ideals and cancellation, are known to hold in the semigroup \betaN where N is the additive semigroup of the integers. We show that these properties are also true in UG for a large class of locally compact groups. The method used is to transfer the information from \betaN --> \betaG where G is an infinite discrete group (or a cancellative commutative semigroup), and then to UG where G is not necessarily discrete.

Date received: June 30, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caao-43.