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On the variety generated by all nilpotent lattice-ordered groups


Authors: V. V. Bludov and A. M. W. Glass
Journal: Trans. Amer. Math. Soc. 358 (2006), 5179-5192
MSC (2000): Primary 06F15, 20F18, 20F12
DOI: https://doi.org/10.1090/S0002-9947-06-03882-7
Published electronically: July 25, 2006
MathSciNet review: 2238913
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Abstract | References | Similar Articles | Additional Information

Abstract: In 1974, J. Martinez introduced the variety $ {\mathcal W}$ of weakly Abelian lattice-ordered groups; it is defined by the identity

$\displaystyle x^{-1}(y\vee 1)x\vee (y\vee 1)^2=(y\vee 1)^2.$


References [Enhancements On Off] (What's this?)

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Additional Information

V. V. Bludov
Affiliation: Institute of Mathematics and Economics, Irkutsk State University, Irkutsk, 664003 Russia
Email: bludov@math.isu.ru

A. M. W. Glass
Affiliation: Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Rd., Cambridge CB3 0WB, England
Email: amwg@dpmms.cam.ac.uk

DOI: https://doi.org/10.1090/S0002-9947-06-03882-7
Keywords: Nilpotent group, residually torsion-free-nilpotent, variety, quasi-variety, commutator calculus, lattice-ordered group, weakly Abelian
Received by editor(s): December 27, 2003
Published electronically: July 25, 2006
Additional Notes: The first author was supported by the Russian Foundation for Basic Research, grant no. 03-01-00320
Dedicated: To Valerie Kopytov on his sixty-fifth birthday
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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