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Minimal sets and varieties |
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| Authors: | Keith A Kearnes Emil W Kiss Matthew A Valeriote |
| Institution: | Department of Mathematics, University of Louisville, Louisville, Kentucky 40292 ; Department of Algebra and Number Theory, Eötvös Lóránd University, 1088 Budapest, Múzeum krt. 6--8, Hungary ; Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada, L8S 4K1 |
| Abstract: | 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 finite, locally solvable varieties. For locally solvable varieties, this solves problems 9 and 10 of Hobby and McKenzie. We generalize part of this result by proving that all locally finite varieties generated by nilpotent algebras that have a trivial locally strongly solvable subvariety are congruence permutable. |
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