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Galois Connections and Applications pp 297–343Cite as

A Survey of Clones Closed Under Conjugation

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Part of the book series: Mathematics and Its Applications ((MAIA,volume 565))

Abstract

There is a Galois connection between the lattice of clones on a set A and the group of permutations on A that is determined by the relation that a permutation conjugates a clone onto itself. The Galois-closed sets on the clone side are the lattices L G of all clones that are closed under conjugation by all members of some permutation group G. In this paper we discuss the coarse structure of the lattice L G when A is finite and G is a 2-homogeneous permutation group, describe L G completely for the case when G is the group of all permutations, and discuss for which groups G the lattice L G is finite.

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Author information

Authors and Affiliations

  1. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720, Szeged, Hungary

    Ágnes Szendrei

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  1. Ágnes Szendrei
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Editors and Affiliations

  1. University of Potsdam, Potsdam, Germany

    K. Denecke

  2. University of Hannover, Hannover, Germany

    M. Erné

  3. University of Lethbridge, Lethbridge, Canada

    S. L. Wismath

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Szendrei, Á. (2004). A Survey of Clones Closed Under Conjugation. In: Denecke, K., Erné, M., Wismath, S.L. (eds) Galois Connections and Applications. Mathematics and Its Applications, vol 565. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-1898-5_8

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  • DOI: https://doi.org/10.1007/978-1-4020-1898-5_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6540-7

  • Online ISBN: 978-1-4020-1898-5

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