On the direct product of $V$-groups
HTML articles powered by AMS MathViewer
- by Donald P. Minassian PDF
- Proc. Amer. Math. Soc. 30 (1971), 434-436 Request permission
Abstract:
Let G and H be ordered groups such that every full order on a subgroup extends to a full order on the group; then the direct product, $G \times H$, need not have this property. In fact a stronger result holds.References
- L. Fuchs and E. Sąsiada, Note on orderable groups, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 7 (1964), 13–17. MR 173715
- M. I. Kargapolov, Completely ordered groups, Algebra i Logika Sem. 1 (1962), no. 2, 16–21 (Russian). MR 0152592
- A. I. Kokorin, On the theory of completely ordered groups, Ural. Gos. Univ. Mat. Zap. 4 (1963), no. tetrad’ 3, 25–29 (1963) (Russian). MR 0183795 D. P. Minassian, Recent developments in the theory of fully ordered groups, Doctoral Thesis, University of Michigan, Ann Arbor, Mich., 1967.
- A. A. Terehov, Completely orderable groups, Dokl. Akad. Nauk SSSR 129 (1959), 34–36 (Russian). MR 0109849
- A. A. Terehov, The structure of locally solvable, completely ordered groups, Algebra i Logika Sem. 1 (1962), no. 2, 10–15 (Russian). MR 0152591
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 434-436
- MSC: Primary 06.75
- DOI: https://doi.org/10.1090/S0002-9939-1971-0286727-5
- MathSciNet review: 0286727