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V. V. Bludov A. M. W. Glass 《Transactions of the American Mathematical Society》2006,358(12):5179-5192
In 1974, J. Martinez introduced the variety of weakly Abelian lattice-ordered groups; it is defined by the identity
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We prove Theorem A. The cardinal product of two copies of the integers is an amalgamation base for the class of all lattice-ordered groups but their lexicographic product is not. This answers Problem 27 of [Black Swamp Problem Book (W. Charles Holland, ed.), Bowling Green State University, 1982]. We also prove Theorem B. he cardinal product of n copies of the integers is not an amalgamation base for the class of all lattice-ordered groups if n ≥ 3. 相似文献
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V. V. Bludov 《Algebra and Logic》2005,44(6):370-380
We give examples of linearly ordered groups that are not embeddable in divisible orderable. In the first example, the group
does not embed in any divisible group with strictly isolated unity. In the second example, the group in question is an O*-group,
and in the third, it is a group with a central system of convex subgroups.
To my teacher A. I. Kokorin
Supported by RFBR grant Nos. 96-01-00358, 99-01-00335, and 03-01-00320.
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Translated from Algebra i Logika, Vol. 44, No. 6, pp. 664–681, November–December, 2005. 相似文献
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Orderable solvable groups in which every relatively convex subgroup is normal are studied. If such a class is subgroup closed
than it is precisely the class of solvable orderable groups which are locally of finite (Mal’tsev) rank. A criterion for an
orderable metabelian group to have every relatively convex subgroup normal is given. Examples of an orderable solvable group
G of length three with periodic G/G′ and of an orderable solvable group of length four with only one proper normal relatively convex subgroup are constructed.
To the memory of N. Ya. Medvedev
Supported by RFBR (project No. 03-01-00320).
Translated from Algebra i Logika, Vol. 48, No. 3, pp. 291–308, May–June, 2009. 相似文献
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In 1963, W. Charles Holland proved that every lattice-ordered group can be embedded in the lattice-ordered group of all order-preserving
permutations of a totally ordered set. In this article we examine the context and proof of this result and survey some of
the many consequences of the ideas involved in this important theorem. 相似文献
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Yu.V. Bludov V.V. Konotop N. Akhmediev 《The European physical journal. Special topics》2010,185(1):169-180
We study numerically rogue waves in the two-component Bose-Einstein condensates which are described by the coupled set of
two Gross-Pitaevskii equations with variable scattering lengths. We show that rogue wave solutions exist only for certain
combinations of the nonlinear coefficients describing two-body interactions. We present the solutions for the combinations
of these coefficients that admit the existence of rogue waves. 相似文献