## Minimal sets and varieties

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- by Keith A. Kearnes, Emil W. Kiss and Matthew A. Valeriote PDF
- Trans. Amer. Math. Soc.
**350**(1998), 1-41 Request permission

## 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.## References

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## Additional Information

**Keith A. Kearnes**- Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
- MR Author ID: 99640
- Email: kakear01@homer.louisville.edu
**Emil W. Kiss**- Affiliation: Department of Algebra and Number Theory, Eötvös Lóránd University, 1088 Budapest, Múzeum krt. 6–8, Hungary
- Email: ewkiss@cs.elte.hu
**Matthew A. Valeriote**- Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada, L8S 4K1
- Email: valeriot@mcmaster.ca
- Received by editor(s): October 14, 1994
- Received by editor(s) in revised form: August 18, 1995
- Additional Notes: This research was partially supported by a fellowship from the Alexander von Humboldt Stiftung (to the first author), by the Hungarian National Foundation for Scientific Research, grant no. 1903 (to the second author), and by the NSERC of Canada (third author)
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**350**(1998), 1-41 - MSC (1991): Primary 08A05; Secondary 08A40, 08B15
- DOI: https://doi.org/10.1090/S0002-9947-98-01594-3
- MathSciNet review: 1348152