On the variety generated by all nilpotent lattice-ordered groups
HTML articles powered by AMS MathViewer
- by V. V. Bludov and A. M. W. Glass PDF
- Trans. Amer. Math. Soc. 358 (2006), 5179-5192 Request permission
Abstract:
In 1974, J. Martinez introduced the variety ${\mathcal W}$ of weakly Abelian lattice-ordered groups; it is defined by the identity \[ x^{-1}(y\vee 1)x\vee (y\vee 1)^2=(y\vee 1)^2.\]References
- V. V. Bludov, On locally nilpotent groups [translation of Trudy Instituta Matematiki, Vol. 30, 26–47, Izdat. Ross. Akad. Nauk, Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1996], Siberian Adv. Math. 8 (1998), no. 1, 49–79. MR 1651902
- V. V. Bludov, A. M. W. Glass, and Akbar H. Rhemtulla, Ordered groups in which all convex jumps are central, J. Korean Math. Soc. 40 (2003), no. 2, 225–239. MR 1958028, DOI 10.4134/JKMS.2003.40.2.225
- V. V. Bludov, A. M. W. Glass, and A. H. Rhemtulla, On centrally orderable groups, J. Algebra 291 (2005), no. 1, 129–143. MR 2158514, DOI 10.1016/j.jalgebra.2005.05.014
- A. M. W. Glass, Partially ordered groups, Series in Algebra, vol. 7, World Scientific Publishing Co., Inc., River Edge, NJ, 1999. MR 1791008, DOI 10.1142/3811
- A. M. W. Glass, Weakly abelian lattice-ordered groups, Proc. Amer. Math. Soc. 129 (2001), no. 3, 677–684. MR 1801994, DOI 10.1090/S0002-9939-00-05706-3
- S. A. Gurchenkov, About varieties of weakly abelian $l$-groups, Math. Slovaca 42 (1992), no. 4, 437–441. MR 1195037
- P. Hall, Nilpotent Groups, Lectures given at the Canadian Mathematical Congress, University of Alberta, 1957.
- V. M. Kopytov, Lattice-ordered locally nilpotent groups, Algebra i Logika 14 (1975), no. 4, 407–413 (Russian). MR 0401583
- V. M. Kopytov and N. Ya. Medvedev, The theory of lattice-ordered groups, Mathematics and its Applications, vol. 307, Kluwer Academic Publishers Group, Dordrecht, 1994. MR 1369091, DOI 10.1007/978-94-015-8304-6
- V. D. Mazurov and E. I. Khukhro (eds.), Unsolved problems in group theory. The Kourovka notebook, Thirteenth augmented edition, Russian Academy of Sciences Siberian Division, Institute of Mathematics, Novosibirsk, 1995. MR 1392713
- Jorge Martinez, Varieties of lattice-ordered groups, Math. Z. 137 (1974), 265–284. MR 354483, DOI 10.1007/BF01214370
- Roberta Botto Mura and Akbar Rhemtulla, Orderable groups, Lecture Notes in Pure and Applied Mathematics, Vol. 27, Marcel Dekker, Inc., New York-Basel, 1977. MR 0491396
- Norman R. Reilly, Nilpotent, weakly abelian and Hamiltonian lattice ordered groups, Czechoslovak Math. J. 33(108) (1983), no. 3, 348–353. MR 718919
- Derek J. S. Robinson, A course in the theory of groups, 2nd ed., Graduate Texts in Mathematics, vol. 80, Springer-Verlag, New York, 1996. MR 1357169, DOI 10.1007/978-1-4419-8594-1
- Robert B. Warfield Jr., Nilpotent groups, Lecture Notes in Mathematics, Vol. 513, Springer-Verlag, Berlin-New York, 1976. MR 0409661
- The Black Swamp Problem Book is edited by W. Charles Holland (Bowling Green State University, Ohio 43403, U.S.A.) and is kept there by him (in the formerly Black Swamp region of Ohio).
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
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2238913
Dedicated: To Valerie Kopytov on his sixty-fifth birthday