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Finite generation of congruence preserving functions

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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Correspondence to Erhard Aichinger.

Additional information

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

Communicated by J. S. Wilson.

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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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Keywords

  • Congruence preserving function
  • Expanded group
  • Clone
  • Finite generation

Mathematics Subject Classification

  • 08A40
  • 08A30