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Ext(Q,Z) is the additive group of real numbers

Published online by Cambridge University Press:  17 April 2009

James Wiegold
James Wiegold
Affiliation:
School of General Studies, Australian National University, Canberra, ACT, and University college of cardiff.
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Abstract

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Standard homological methods and a theorem of Harrison on cotorsion groups are used to prove the result mentioned.

In this note Z denotes an infinite cyclic group, Q the additive group of rational numbers, Zp ∞ a p–quasicyclie group, and Ip the group of p–adic integers.

Pascual Llorente proves in [3] that Ext(Q,z) is an uncountable group, and gives explicitly a countably infinite subset. Very little extra effort produces the result embodied in the title, as follows.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 3 , December 1969 , pp. 341 - 343
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Fuchs, L., Abelian groups (Publishing House of the Hungarian Academy of Sciences, Budapest, 1958).Google Scholar
[2]Harrison, D.K., ‘Infinite abelian groups and homological methods’, Ann. of Math. 69 (1959), 366–391.CrossRefGoogle Scholar
[3]Llorente, Pascual, ‘Construccion de grupos-estensiones’, Univ. Nac. Ingen. Inst. Mat. Puras Apl. Notas Mat. 4 (1966), 119–145.Google Scholar