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Uniqueness in Structure Theorems for LCA Groups

Published online by Cambridge University Press:  20 November 2018

D. L. Armacost and
W. L. Armacost
D. L. Armacost
Affiliation:
Amherst College, Amherst, Massachusetts
W. L. Armacost
Affiliation:
California State University at Dominguez Hills, Dominguez Hills, California
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The classical Pontrjagin-van Kampen structure theorem states that any locally compact abelian (LCA) group G can be written as the direct product of a vector group Rm (where R denotes the additive group of real numbers with the usual topology, and m is a non-negative integer) and an LCA group H which contains a compact open subgroup. This important theorem, which van Kampen deduced from the work of Pontrjagin, was first stated and proved in [5, p. 461].

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 3 , 01 June 1978, pp. 593 - 599
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Armacost, D., Sufficiency classes of LCA groups, Trans. Amer. Math. Soc. 158 (1971), 331–338.Google Scholar
2. Braconnier, J., Sur les groupes topologiques localement compacts, J. Math. Pures Appl., N.S. 27 (1948), 1–85.Google Scholar
3. Corwin, L., Some remarks on self-dual locally compact abelian groups, Trans. Amer. Math. Soc. 148 (1970), 613–622.Google Scholar
4. Hewitt, E. and Ross, K., Abstract harmonie analysis, Vol. 1 (Academic Press, New York, 1963).Google Scholar
5. van Kampen, E., Locally bicompact groups and their character groups, Ann. of Math. (2) 30 (1935), 448–463.Google Scholar
6. Pontrjagin, L., Topological groups (Princeton University Press, Princeton, 1939).Google Scholar
7. Robertson, L., Connectivity, divisibility, and torsion, Trans. Amer. Math. Soc. 128 (1967), 482–505.Google Scholar
8. Robertson, L., Transfinite torsion, p-constituents, and splitting in locally compact abelian groups c. (1968, unpublished).Google Scholar