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A remark on elementary abelian groups

Published online by Cambridge University Press:  17 April 2009

J.L. Hickman
J.L. Hickman
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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Dr M.F. Newman has asked whether in the absence of the Axiom of Choice it is possible to have two non-isomorphic elementary abelian groups of the same (finite) exponent and of the same (infinite) cardinality. By means of an example, I show that this is in fact possible, if the exponent is at least five; I do not know the answer in the remaining two cases. The example given requires the construction of a Fraenkel-Mostowski model of set theory, and for this purpose I draw upon the terminology, constructions, and results contained in the first two sections of a previous paper, “The construction of groups in models of set theory that fail the Axiom of Choice” (Bull. Austral. Math. Soc. 14 (1976), 199–232), with which I assume familiarity.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 2 , April 1977 , pp. 213 - 217
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Hickman, J.L., “The construction of groups in models of set theory that fail the Axiom of Choice”, Bull. Austral. Math. Soc. 14 (1976), 199–232.CrossRefGoogle Scholar