Finitely generated clones of congruence preserving functions
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
AAA89 - 89. Arbeitstagung Allgemeine Algebra
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
We investigate for which algebras the clone of congruence
preserving functions is finitely generated.
Finite abelian groups provide examples for both
alternatives: for example,
$\mathbb{Z}_{45}$ and $\mathbb{Z}_{27} \times \mathbb{Z}_{125} \times \mathbb{Z}_{125} \times \mathbb{Z}_5$
have a finitely generated clone of congruene preserving functions,
whereas the clone of congruence preserving functions
of $\mathbb{Z}_{125} \times \mathbb{Z}_5$ is not finitely generated.
We will give a complete description for finite abelian groups and
for finite $p$-groups.
(Joint research with Marijana Lazi\'c and Neboj\v{s}a Mudrinski,
Novi Sad)