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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Minimal sets and varieties


Authors: Keith A. Kearnes, Emil W. Kiss and Matthew A. Valeriote
Journal: Trans. Amer. Math. Soc. 350 (1998), 1-41
MSC (1991): Primary 08A05; Secondary 08A40, 08B15
MathSciNet review: 1348152
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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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Additional Information

Keith A. Kearnes
Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
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

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01594-3
PII: S 0002-9947(98)01594-3
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)
Article copyright: © Copyright 1998 American Mathematical Society