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The type set of a torsion-free abelian group of rank two

Part of: Abelian groups

Published online by Cambridge University Press:  09 April 2009

David R. Jackett
David R. Jackett
Affiliation:
University of TasmaniaHobart, Australia
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Abstract

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In this paper we generalize a recent result of Freedman (1973) concerning the cardinality of the type set of a rank two torsion-free abelian group. We show that if A is such a group and A supports a non-trivial associative ring then the type set of A contains at most three elements.

MSC classification

Secondary: 20K15: Torsion-free groups, finite rank
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 4 , June 1979 , pp. 507 - 510
Copyright
Copyright © Australian Mathematical Society 1979

References

Beaumont, R. A. and Wisner, R. J. (1959), ‘Rings with additive group which is a torsion-free group of rank two’, Acta Sci. Math. (Szeged) 20, 105–116.Google Scholar
Feigelstock, S. (1976), ‘On the type set of groups and nilpotence’, Comment. Math. Univ. St. Paul 25, 159–165.Google Scholar
Freedman, H. (1973), ‘On the additive group of a torsion-free ring of rank two’, Publ. Math. Debrecen 20, 85–87.CrossRefGoogle Scholar
Fuchs, L. (1973), Infinite abelian groups, Vol. II (Academic Press, New York).Google Scholar