Converting Groups into Cancellative Semigroups: an Algebraic Approach to the Wallace Problem
by
Douglass L. Grant
University College of Cape Breton

It has been shown by Robbie and Svetlichny under CH and by Tomita under a version of MA that it is possible to construct a countably compact, cancellative topological semigroup which is not a group. The question remains open as to whether such a construction is possible in ZFC. We explore the possibility of redefining the binary operation on a countably compact topological group so that the result is a cancellative semigroup with continuous operation which fails to be a group.

Date received: June 24, 1996

Copyright © 1996 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 # caah-25.