Finite generation of congruence preserving functions (Q314481)

Property \(P\) of an algebra to have a finitely generated clone of congruence-preserving functions is investigated. Among the following algebras those having property \(P\) are characterized: finite \(p\)-groups, finite nilpotent groups, certain finite expanded groups as well as finite algebras having a Mal'cev term and a simple congruence lattice. For certain expanded groups a sufficient condition for having property \(P\) is provided. Here, an expanded group is an algebra having a reduct of type \((2,1,0)\) being a group.