Minimal sets and varieties

The aim of this paper is twofold. First some machinery is established to reveal the structure of abelian congruences. Then we describe all minimal, locally nite, locally solvable varieties. For locally solvable varieties, this solves problems 9 and 10 of Hobby and McKenzie, [6]. We generalize part of this result by proving that all locally nite varieties generated by nilpotent algebras that have a trivial locally strongly solvable subvariety are congruence permutable.

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