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Finite generation of congruence preserving functions

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Abstract

We investigate when the clone of congruence preserving functions is finitely generated. We obtain a full description for all finite p-groups, and for all finite algebras with Mal’cev term and simple congruence lattice. The characterization for p-groups allows a generalization to a large class of expansions of groups.

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Acknowledgments

We thank J. Farley, K. Kaarli, and C. Pech for fruitful discussions on parts of this paper, and the referee for numerous valuable suggestions.

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Authors and Affiliations

  1. Institut für Algebra, Johannes Kepler Universität Linz, 4040, Linz, Austria

    Erhard Aichinger, Marijana Lazić & Nebojša Mudrinski

  2. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia

    Marijana Lazić & Nebojša Mudrinski

Authors
  1. Erhard Aichinger
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  2. Marijana Lazić
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  3. Nebojša Mudrinski
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Correspondence to Erhard Aichinger.

Additional information

Communicated by J. S. Wilson.

Supported by Austrian research fund FWF P24077 and Research Grant 174018 of the Ministry of Science and Education of the Republic of Serbia.

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Aichinger, E., Lazić, M. & Mudrinski, N. Finite generation of congruence preserving functions. Monatsh Math 181, 35–62 (2016). https://doi.org/10.1007/s00605-015-0833-5

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  • DOI: https://doi.org/10.1007/s00605-015-0833-5

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