A Reduced Spectrum for Isolated Groups
by
Néstor G. Martínez
Department of Mathematics, University of Buenos Aires
Coauthors: Alejandro Petrovich (Department of Mathematics, University of Buenos Aires)

In a previous work the authors have developed a Priestley-type topological representation for the class of partially ordered groups which are partially ordered subgroups of lattice-ordered groups. The appropriate analog of the spectrum of prime lattice filters happens to be the class of increasing subsets P satisfying ab belongs to P and cd belongs to P imply ad belongs to P or cb belongs to P. In developing this representation new embedding theorems for these groups were obtained. The construction gives also an alternative and very natural way to obtain the free l-group generated by a p.o.group. As a continuation of these ideas different subfamilies of this spectrum are studied. A reduced spectrum with a simpler description is obtained. This spectrum is a disjoint union of chains, with an involution in each chain, from which the group structure can be still recovered.

Date received: December 9, 2002

Copyright © 2002 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 # cakg-07.