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The extension of partially ordered groups. (English) Zbl 0039.25201


Keywords:

group theory
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[1] O. Schreier, Über die Erweiterung von Gruppen, I:Monatshefte Math. Phys.,34 (1926), pp. 165–180; II:Hamburger Abh.,4 (1926), pp. 321–346. · JFM 52.0113.04
[2] For example, the extension theory for rings was given byC. J. Everett Jr, An extension theory for rings,Amer. J. Math.,64 (1942), pp. 363–370. Independently ofEverett, T. Szele discovered the same extension theory. · Zbl 0060.07601
[3] In a very special caseG. Birkhoff has given a method for constructing certain, but not all extensions. See his paper: Lattice-ordered groupsAnnals Math.,43 (1942), pp. 298–331.
[4] See e. g.C. J. Everett andS. Ulam, On ordered groups,Trans. Amer. Math., Soc.,57 (1945), pp. 208–216. · Zbl 0061.03406
[5] For a detailed discussion see my paper: On partially ordered groups,Proc. Kon. Nederl. Akad. v. Wetensch.,53 (1950), pp. 828–834.
[6] A(C) denotes the group of allo-automorphisms ofC.
[7] We observe that if one assumes theMS-property both inC and inF, then the extension group will also have theMS-property. The proof is immediate.
[8] Henceforth we shall identifyC * withC.
[9] See loc. cit. On partially ordered groups,Proc. Kon. Nederl. Akad. v. Wetensch.,53 (1950), pp. 828–834.
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