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$$C$$-clones and $$C$$-automorphism groups. (English) Zbl 1229.08002
Chajda, I. (ed.) et al., Proceedings of the 79th workshop on general algebra “79. Arbeitstagung Allgemeine Algebra”, 25th conference of young algebraists, Palacký University Olomouc, Olomouc, Czech Republic, February 12–14, 2010. Klagenfurt: Verlag Johannes Heyn (ISBN 978-3-7084-0407-3/pbk). Contributions to General Algebra 19, 1-12 (2010).
The authors classify the lattice of the so-called $$C$$-clones on a finite set up to equality of the automorphism part of their members. A $$C$$-clone is a clone which is determined by a set of clausal relations defined in the paper. It is shown that the precondition of bijectivity imposes such strong constraints on the $$C$$-clone lattice that the resulting lattice is fairly well-behaved. It is proved that the Krasner clones corresponding to the $$C$$-automorphism groups are determined by some of their unary relations which are intervals on the base set. They form a Boolean lattice whose automorphism group can be constructed as a direct product of the symmetric groups of these intervals.
For the entire collection see [Zbl 1201.08001].

##### MSC:
 08A40 Operations and polynomials in algebraic structures, primal algebras 08A02 Relational systems, laws of composition 08A35 Automorphisms and endomorphisms of algebraic structures 06A15 Galois correspondences, closure operators (in relation to ordered sets)