Nilpotence, twin groups, and an application
by
Emil W. Kiss
Department of Algebra and Number Theory, Eotvos University, Budapest, Hungary

Among the various extensions of tame congruence theory, one of the most important ones is the theory of nilpotence. Strongly related to this is the concept of the twin group, consisting of the twins of the identity map on a subset of the algebra. These groups help to describe various aspects of nilpotence, and are related to such important properties as residual smallness, or free spectra. The talk will give a short introduction to these concepts, which will hopefully be useful to newcomers to this area, too. Then, as an application, we shall proceed to see how these concepts help to investigate algebras generating a variety with definable principal congruences.

Date received: June 30, 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 # caiv-40.