# Classification of self-dual torsion-free LCA groups

Fundamenta Mathematicae (1992)

- Volume: 140, Issue: 3, page 255-278
- ISSN: 0016-2736

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topWu, S.. "Classification of self-dual torsion-free LCA groups." Fundamenta Mathematicae 140.3 (1992): 255-278. <http://eudml.org/doc/211945>.

@article{Wu1992,

abstract = {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.},

author = {Wu, S.},

journal = {Fundamenta Mathematicae},

keywords = {self-dual torsion free LCA groups; self-dual divisible LCA groups},

language = {eng},

number = {3},

pages = {255-278},

title = {Classification of self-dual torsion-free LCA groups},

url = {http://eudml.org/doc/211945},

volume = {140},

year = {1992},

}

TY - JOUR

AU - Wu, S.

TI - Classification of self-dual torsion-free LCA groups

JO - Fundamenta Mathematicae

PY - 1992

VL - 140

IS - 3

SP - 255

EP - 278

AB - 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.

LA - eng

KW - self-dual torsion free LCA groups; self-dual divisible LCA groups

UR - http://eudml.org/doc/211945

ER -

## References

top- [1] D. L. Armacost, The Structure of Locally Compact Abelian Groups, Marcel Dekker, New York 1981. Zbl0509.22003
- [2] L. Corwin, Some remarks on self-dual locally compact Abelian groups, Trans. Amer. Math. Soc. 148 (1970), 613-622. Zbl0198.34903
- [3] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis I, Springer, New York 1979. Zbl0416.43001
- [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. Zbl0195.04603
- [6] N. W. Rickert, The structure of a class of locally compact abelian groups, unpublished (1968). Zbl0177.18201
- [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.

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