Extensions of locally compact abelian groups. II
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- by Ronald O. Fulp and Phillip A. Griffith PDF
- Trans. Amer. Math. Soc. 154 (1971), 357-363 Request permission
Abstract:
It is shown that the extension functor defined on the category $\mathcal {L}$ of locally compact abelian groups is right-exact. Actually ${\text {Ext}^n}$ is shown to be zero for all $n \geqq 2$. Various applications are obtained which deal with the general problem as to when a locally compact abelian group is the direct product of a connected group and a totally disconnected group. One such result is that a locally compact abelian group G has the property that every extension of G by a connected group in $\mathcal {L}$ splits iff $G = {(R/Z)^\sigma } \oplus {R^n}$ for some cardinal $\sigma$ and positive integer n.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 154 (1971), 357-363
- MSC: Primary 18.20; Secondary 22.00
- DOI: https://doi.org/10.1090/S0002-9947-1971-0272870-8
- MathSciNet review: 0272870