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arXiv · 1610.01800

Congruence lattices forcing nilpotency

Erhard Aichinger
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Abstract

Given a lattice $\mathbb{L}$ and a class $K$ of algebraic structures, we say that $\mathbb{L}$ \emph{forces nilpotency} in $K$ if every algebra $\mathbf{A} \in K$ whose congruence lattice $\mathrm{Con} (\mathbf{A})$ is isomorphic to $\mathbb{L}$ is nilpotent. We describe congruence lattices that force nilpotency, supernilpotency or solvability for some classes of algebras. For this purpose, we investigate which commutator operations can exist on a given congruence lattice.

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Erhard Aichinger. 2016-10-06. Congruence lattices forcing nilpotency. https://doi.org/10.1142/s0219498818500330

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