Classification of self-dual torsion-free LCA groups

• Autorzy: S. L. Wu
• Języki publikacji: EN

Abstrakty

EN

In this paper we seek to describe the structure of self-dual torsion-free LCA groups. We first present a proof of the structure theorem of self-dual torsion-free metric LCA groups. Then we generalize the structure theorem to a larger class of self-dual torsion-free LCA groups. We also give a characterization of torsion-free divisible LCA groups. Consequently, a complete classification of self-dual divisible LCA groups is obtained; and any self-dual torsion-free LCA group can be regarded as an open subgroup of a well-understood torsion-free divisible LCA group.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1991-1992
• Tom: 140
• Numer: 3
• Strony: 255-278

Daty

wydano

1992

otrzymano

1991-07-01

Twórcy

autor

S. L. Wu

• Department of Mathematics, University of Oregon, Eugene, Oregon 97403, U.S.A.

Bibliografia

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• [2] L. Corwin, Some remarks on self-dual locally compact Abelian groups, Trans. Amer. Math. Soc. 148 (1970), 613-622.
• [3] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis I, Springer, New York 1979.
• [4] L. S. Pontryagin, Topological Groups, 2nd ed., Gordon and Breach, New York 1966.
• [5] M. Rajagopalan and T. Soundararajan, Structure of self-dual torsion-free metric LCA groups, Fund. Math. 65 (1969), 309-316.
• [6] N. W. Rickert, The structure of a class of locally compact abelian groups, unpublished (1968).
• [7] L. C. Robertson, Connectivity, divisibility, and torsion, Trans. Amer. Math. Soc. 128 (1967), 482-505.
• [8] N. Ya. Vilenkin, Direct decomposition of topological groups, Amer. Math. Soc. Transl. (1) 8 (1962), 79-185.