Monatshefte für Mathematik

, Volume 181, Issue 1, pp 35–62 | Cite as

Finite generation of congruence preserving functions

  • Erhard AichingerEmail author
  • Marijana Lazić
  • Nebojša Mudrinski


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.


Congruence preserving function Expanded group Clone  Finite generation 

Mathematics Subject Classification

08A40 08A30 



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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Copyright information

© Springer-Verlag Wien 2015

Authors and Affiliations

  • Erhard Aichinger
    • 1
    Email author
  • Marijana Lazić
    • 1
    • 2
  • Nebojša Mudrinski
    • 1
    • 2
  1. 1.Institut für AlgebraJohannes Kepler Universität LinzLinzAustria
  2. 2.Department of Mathematics and Informatics, Faculty of SciencesUniversity of Novi SadNovi SadSerbia

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