Locally solvable factors of varieties

Author:
Keith A. Kearnes

Journal:
Proc. Amer. Math. Soc. **124** (1996), 3619-3625

MSC (1991):
Primary 08B25; Secondary 08A05

DOI:
https://doi.org/10.1090/S0002-9939-96-03501-0

MathSciNet review:
1343705

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Abstract | References | Similar Articles | Additional Information

Abstract: We give necessary and sufficient local conditions, which are easy to check, for a locally finite variety to decompose as the product of a locally solvable subvariety and a subvariety which has type set disjoint from the type set of .

**1.**P. Agliano and K. A. Kearnes,*Congruence semimodular varieties I: locally finite varieties*, Algebra Universalis**32**(1994), 224-269. MR**95i:08010****2.**R. Freese and R. McKenzie,*Commutator Theory for Congruence Modular Varieties*, LMS Lecture Notes v. 125, Cambridge University Press, 1987. MR**89c:08006****3.**D. Hobby and R. McKenzie,*The Structure of Finite Algebras*, Contemporary Mathematics v. 76, American Mathematical Society, 1988. MR**89m:08001****4.**K. A. Kearnes,*A Hamiltonian property for nilpotent algebras*, to appear in Algebra Universalis.**5.**R. McKenzie and M. Valeriote,*The Structure of Decidable Locally Finite Varieties*, Progress in Mathematics v. 79, Birkhäuser, 1989. MR**92j:08001****6.**M. Valeriote,*On Decidable Locally Finite Varieties*, Ph. D. Dissertation, U. C. Berkeley, 1986.

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Additional Information

**Keith A. Kearnes**

Affiliation:
Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701

Email:
kearnes@comp.uark.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03501-0

Received by editor(s):
September 7, 1994

Received by editor(s) in revised form:
June 5, 1995

Additional Notes:
Research supported by a fellowship from the Alexander von Humboldt Stiftung.

Communicated by:
Lance W. Small

Article copyright:
© Copyright 1996
American Mathematical Society