Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

SCImago Journal Rank (SJR) 2018: 0.279
Source Normalized Impact per Paper (SNIP) 2018: 0.627

Mathematical Citation Quotient (MCQ) 2018: 0.29

See all formats and pricing
More options …
Volume 64, Issue 3


Amalgamation bases for the class of lattice-ordered groups

V. Bludov
  • Department of Mathematics Physics, and Informatics Irkutsk State Teachers, Training University, Irkutsk, 664011, Russia
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ A. Glass
Published Online: 2014-07-05 | DOI: https://doi.org/10.2478/s12175-014-0227-5


We prove

TheoremA. 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

TheoremB. 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.

MSC: Primary 06F15; Secondary 20E06

Keywords: amalgamation; lattice-ordered group; ℓ-permutation group

  • [1] BLUDOV, V. V.: On free products of right-ordered groups with amalgamated subgroup. In: Problems of Modern Mathematics, Proc. Scientific Works, V.II, NII MIOO NGU, Novosibirsk, 1966, pp. 30–35 (Russian). Google Scholar

  • [2] BLUDOV, V. V.— GLASS, A. M. W.: Conjugacy in lattice-ordered groups and right-ordered groups, J. Group Theory 11 (2008), 623–633. http://dx.doi.org/10.1515/JGT.2008.038Web of ScienceCrossrefGoogle Scholar

  • [3] BLUDOV, V. V.— GLASS, A. M. W.: Right orders and amalgamation for lattice-ordered groups, Math. Slovaca 61 (2011), 355–372. http://dx.doi.org/10.2478/s12175-011-0017-2CrossrefWeb of ScienceGoogle Scholar

  • [4] GLASS, A. M. W.: Partially Ordered Groups. Series in Algebra 7, World Scientific Publ. Co., Singapore, 1999. Google Scholar

  • [5] HOLLAND, W. C.: The lattice-ordered group of automorphisms of an ordered set, Michigan Math. J. 10 (1963), 399–408. http://dx.doi.org/10.1307/mmj/1028998976CrossrefGoogle Scholar

  • [6] HOLLAND, W. C.: Group equations which hold in lattice-ordered groups, Symposia Math. XXI (1977), 365–378. Google Scholar

  • [7] MEDVEDEV, N. Ya.: Quasivarieties of ℓ-groups and groups, Sib. Math. J. 26 (1985), 717–722. http://dx.doi.org/10.1007/BF00969031CrossrefGoogle Scholar

  • [8] PIERCE, K. R.: Amalgamations of lattice-ordered groups, Trans. Amer.Math. Soc. 172 (1972), 249–260. http://dx.doi.org/10.1090/S0002-9947-1972-0325488-3CrossrefGoogle Scholar

  • [9] POWELL, W. B.— TSINAKIS, C.: Amalgamations of lattice-ordered groups. In: Ordered Algebraic Structures (W. B. Powell, C. Tsinakis, eds.). Lecture Notes in Pure and Appl. Algebra, Vol. 99, Marcel Dekker, New York-Basel, 1982, pp. 171–178. Google Scholar

  • [10] WIEGOLD, J.: Nilpotent products of groups with amalgamations, Publ. Math. Debrecen 6 (1959), 131–168. Google Scholar

  • [11] Black Swamp Problem Book (W. Charles Holland, ed.), Bowling Green State University, 1982. Google Scholar

About the article

Published Online: 2014-07-05

Published in Print: 2014-06-01

Citation Information: Mathematica Slovaca, Volume 64, Issue 3, Pages 571–578, ISSN (Online) 1337-2211, DOI: https://doi.org/10.2478/s12175-014-0227-5.

Export Citation

© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in