Finite generation of congruence preserving functions

TL;DR

This paper characterizes when the set of congruence preserving functions is finitely generated, providing full descriptions for finite p-groups and certain finite algebras, with implications for group expansions.

Contribution

It offers a complete characterization of finite generation of congruence preserving functions for specific algebraic structures, extending previous results.

Findings

Full description for finite p-groups

Characterization for finite algebras with Mal'cev term

Generalization to expansions of groups

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.