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2003 Summer Conference on Topology and its Applications
July 9-12, 2003
Howard University
Washington, DC, USA

Organizers
Neil Hindman, Joshua Leslie, Amir Maleki, Thierry Robart, Sherif El-Helaly, John Kulesza, Salvador Garcia-Ferreira, Javier Trigos-Arrietta, Grant Woods, Alan Dow, Judy Kennedy, Randall McCutcheon Karl Hofmann, Dona Strauss, Jimmie Lawson, Michael Mislove

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\omega-groups
by
J. D. Reid
Wesleyan University

The groups of the title are those infinite abelian groups of cardinality k that have fewer than 2k subgroups. These arose (Berhanu, Comfort, Reid, Pac. J. Math., 1985) in investigating the number of topological group topologies of various kinds a given abelian group might support. It turns out that an \omega-group is necessarily countable with countably many subgroups. We will review certain structural results on these groups, and then give some invariants for the groups, methods of constructing them, and some results on their endomorphism rings. These extend the earlier investigation and provide a natural context for "classical" examples of Arnold and of Pierce.

Date received: June 18, 2003

Copyright © 2003 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 # calv-04.