Abstract
We prove that in a locally finite variety with the congruence extension property, locally solvable congruences are central and locally solvable algebras are Hamiltonian. Also, we prove that a maximal subuniverse of a finite algebra in an Abelian variety is identical with an equivalence class of some congruence.
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McKenzie, R. Congruence extension, Hamiltonian and Abelian properties in locally finite varieties. Algebra Universalis 28, 589–603 (1991). https://doi.org/10.1007/BF01195865
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DOI: https://doi.org/10.1007/BF01195865