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Conference in Algebra (in honour of the 70th birthday of Ervin Fried)
August 17-21, 1999
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences
Budapest, Hungary

Organizers
László Márki

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Permutations and Finite Algebras
by
Ágnes Szendrei
Bolyai Institue, University of Szeged

Let \Gamma be a permutation group acting on a finite set A. Suppose we want to expand the unary algebra (A;\Gamma) with operations in such a way that the resulting algebra has no unary term operations other than those in \Gamma. We present results showing that for several interesting classes of permutation groups

(i)
a proper expansion is impossible, or
(ii)
the possible expansions are limited, and the resulting algebras can be completely described.
Clone theoretical results of this kind are used in the analysis of the structure of finite algebras.

Date received: July 30, 1999

Copyright © 1999 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 # cadj-21.