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

  • James Wiegold (a1)
Abstract

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.

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References
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[1]Fuchs L., Abelian groups (Publishing House of the Hungarian Academy of Sciences, Budapest, 1958).
[2]Harrison D.K., ‘Infinite abelian groups and homological methods’, Ann. of Math. 69 (1959), 366391.
[3]Llorente Pascual, ‘Construccion de grupos-estensiones’, Univ. Nac. Ingen. Inst. Mat. Puras Apl. Notas Mat. 4 (1966), 119145.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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