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Clones and weak automorphisms
by
László Szabó
University of Szeged
By (an automorphism) a weak automorphism of a clone F on a set A we mean a permutation \pi in A such that for every f in F we have (f\pi=f) f\pi, f\pi-1 in F, where f\pi(x1, ... , xn)=f(x1\pi-1, ... , xn\pi-1)\pi for all x1, ... , xn in A. The set of all (automorphisms) weak automorphisms of F form a permutation group (Aut F) WAut F such that Aut F\triangleleftWAut F, and F \cap SA\triangleleftWAut F if A is finite. Some results on weak automorphisms of clones are presented. Among others, a classification is given for the clones on a finite set A whose groups of weak automorphisms are SA.
Date received: May 22, 2000
Copyright © 2000 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 # caee-49.