Abstract
We study a certain application of the theory of characters for commutative compact topological groups and weakly linearly compact groups.
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References
L. Fuchs, Infinite Abelian Groups, Vol. 1, Pure Appl. Math., 36, Academic Press, New York–London (1970).
E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. I. Structure of Topological Groups. Integration Theory, Group Representations, Grundlehren Math. Wissenschaften, 115, Academic Press, New York; Springer-Verlag, Berlin–Gottingen–Heidelberg (1963).
A. Hulanicki, “Algebraic characterization of abelian divisible groups which admit compact topologies,” Fund. Math., 44, 192–197 (1957).
L. Koulikoff, “On the theory of Abelian groups of arbitrary power,” Mat. Sb., 16 (58), 129–162 (1945).
S. A. Morris, Pontryagin Duality and the Structure of Locally Compact Abelian Groups, London Math. Soc. Lect. Notes, 29, Cambridge Univ. Press, Cambridge (1977).
L. S. Pontryagin, Continuous Groups [in Russian], GITTL, Moscow (1954).
M. Rajagopalan, “Structure of monogenic groups,” Ill. J. Math., 12, 205–214 (1968).
M. Rajagopalan and T. Soundararajan, “Structure of self-dual torsion-free metric LCA groups,” Fund. Math., 65, 309–316 (1969).
O. E. Surmanidze, “Weakly linearly compact topological abelian groups,” Tr. Tbilis. Mat. Inst. Razmadze Akad. Nauk Gruz. SSR, 46, 77–108 (1975).
O. E. Surmanidze, “Direct decompositions of locally compact abelian groups,” Soobshch. Akad. Nauk Gruz. SSR, 89, No. 2, 293–295 (1978).
O. E. Surmanidze, “Direct decomposition of linearly discrete abelian groups,” Soobshch. Akad. Nauk Gruz. SSR, 89, No. 3, 529–532 (1978).
O. E. Surmanidze, “On some properties of compact and weakly locally compact topological abelian groups,” Tr. Tbilis. Mat. Inst. Razmadze Akad. Nauk Gruz. SSR, 70, 108–115 (1982).
N. Ya. Vilenkin, “The theory of topological groups, II. Direct products. Direct sums of groups of order 1. Locally compact Abelian groups. Fibered and weakly separable groups,” Usp. Mat. Nauk, 5, No. 4 (38), 19–74 (1950).
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 74, Proceedings of the International Conference “Modern Algebra and Its Applications” (Batumi, 2010), Part 1, 2011.
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Surmanidze, O. On a certain application of the theory of characters for commutative groups. J Math Sci 186, 805–807 (2012). https://doi.org/10.1007/s10958-012-1038-2
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DOI: https://doi.org/10.1007/s10958-012-1038-2