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On Convex Subgroups of Groups with the Interpolation Property

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Abstract

Characteristics of groups with the interpolation relation (not necessarily directed) are considered. A necessary and sufficient condition for a partially ordered group to be an interpolation group is obtained. An almost orthogonality criterion for positive elements of an interpolation group is proved. Characteristics of minimal convex directed subgroups containing almost orthogonal elements are described. Properties of convex directed subgroups in the subclass of interpolation groups in which each element is a quotient of two almost orthogonal elements are investigated.

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References

  1. P. Conrad, “Representation of partially ordered Abelian groups as groups of real valued functions,” Acta Math., 116, 199–221 (1966).

    MATH  MathSciNet  Google Scholar 

  2. L. Fuchs, Partially Ordered Algebraic Systems, Pergamon Press, Oxford; Addison-Wesley, Reading (1963).

  3. L. Fuchs, “Riesz groups,” Ann. Scuola Norm. Sup. Pisa, 19, No. 3, 1–34 (1965).

    MATH  MathSciNet  Google Scholar 

  4. A. M. W. Glass, “Polars and their application in directed interpolation groups,” Trans. Am. Math. Soc., 166, 1–25 (1972).

    Article  MATH  MathSciNet  Google Scholar 

  5. V. M. Kopytov, Lattice-Ordered Groups [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  6. S. Lang, Algebra, Addison-Wesley, Reading (1965).

    MATH  Google Scholar 

  7. E. E. Shirshova, “Pseudo-lattice ordered groups,” in: Groups and Modules; Game Theory [in Russian], Moskovsk. Oblast. Ped. Inst., Moscow (1973), pp. 10–18.

  8. E. E. Shirshova, “Associated subgroups of pseudo-lattice ordered groups,” in: Algebraic Systems [in Russian], Ivanovsk. Gos. Univ., Ivanovo (1991), pp. 78–85.

  9. E. E. Shirshova, “Properties of homomorphisms of Riesz groups,” Usp. Mat. Nauk, 46, No. 5 (281), 157–158 (1991).

    MATH  MathSciNet  Google Scholar 

  10. E. E. Shirshova, “Lexicographic extensions and pl-groups,” Fundam. Prikl. Mat., 1, No. 4, 1133–1138 (1995).

    MATH  MathSciNet  Google Scholar 

  11. E. E. Shirshova, “On homomorphisms of pl-group,” Fundam. Prikl. Mat., 3, No. 1, 303–314 (1997).

    MATH  MathSciNet  Google Scholar 

  12. E. E. Shirshova, “Homomorphisms which preserve p-disjointness,” Fundam. Prikl. Mat., 6, No. 3, 939–952 (2000).

    MATH  MathSciNet  Google Scholar 

  13. E. E. Shirshova, “On groups with the almost orthogonality condition,” Commun. Algebra, 28, No. 10, 4803–4818 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  14. E. E. Shirshova, “On a generalization of the notion of orthogonality and on the Riesz groups,” Math. Notes, 69, No. 1, 107–115 (2001).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Moscow Pedagogical State University, Moscow, Russia

    E. E. Shirshova

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  1. E. E. Shirshova
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Correspondence to E. E. Shirshova.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 7, pp. 187–199, 2011/12.

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Shirshova, E.E. On Convex Subgroups of Groups with the Interpolation Property. J Math Sci 197, 573–581 (2014). https://doi.org/10.1007/s10958-014-1736-z

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