Splitting of extensions in the category of locally compact abelian groups

Sahleh, Hossein; Alijani, Akbar

doi:10.22108/ijgt.2014.4435

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	Splitting of extensions in the category of locally compact abelian groups
International Journal of Group Theory
مقاله 4، دوره 3، شماره 3، آذر 2014، صفحه 39-45 اصل مقاله (274.47 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2014.4435
نویسندگان
Hossein Sahleh^* ¹؛ Akbar Alijani²
¹Department of Mathematics University of Guilan
²University of Guilan
چکیده
Let $\pounds$ be the category of all locally compact abelian (LCA) groups‎. ‎In this paper‎, ‎the groups $G$ in $\pounds$ are determined such that every extension $0\to X\to Y\to G\to 0$ with divisible‎, ‎$\sigma-$compact $X$ in $\pounds$ splits‎. ‎We also determine the discrete or compactly generated LCA groups $H$ such that every pure extension $0\to H\to Y\to X\to 0$ splits for each divisible group $X$ in $\pounds$‎.
کلیدواژه‌ها
Locally compact abelian group؛ Splitting of Extension؛ Divisible group

مراجع
D. L. Armacost (1981) The structure of locally compact abelian groups Marcel Dekker Inc., New York 68 J. Braconnier (1948) Sur les groupes topologiques localement compacts J. Math. Pures Appl. (9) 27, 1-85 J. Dixmier (1957) Quelques proprietes des groupes abeliens localement compacts Bull. Sci. Math. 81, 38-48 L. Fuchs (1970) Infinite Abelian Groups Pure and Applied Mathematics, Academic Press, New York-London 36 R. O. Fulp (1970) Homological study of purity in locally compact groups Proc. London Math. Soc. (3) 21, 502-512 R. O. Fulp (1972) Splitting locally compact abelian groups Michigan Math. J. 19, 47-55 R. O. Fulp and P. Griffith (1971) Extensions of locally compact abelian groups. I Trans. Amer. Math. Soc. 154, 341-356 R. O. Fulp and P. Griffith (1971) Extensions of locally compact abelian groups II Trans. Math. Soc. 154, 357-363 S. Hartman and A. Hulanicki (1957) Les sous-groupes purs et leurs duals Fund. Math. 45, 71-77 E. Hewitt and K. Ross (1979) Abstract Harmonic Analysis Second Edition, Springer Verlag, Berlin-New York I P. Loth (2001) Topologically pure extensions. Abelian groups, rings and modules, Contemp. Math., Providence, RI Amer. Math. Soc. 273, 191-201 P. Loth (2003) On pure subgroups of locally compact abelian groups Arch. Math. (Basel) 81, 255-257 P. Loth (2006) Pure extensions of locally compact abelian groups Rend. Sem. Mat. Univ. Padova 116, 31-40 M. Moskowitz (1967) Homological algebra in locally compact abelian groups Trans. Amer. Math. Soc. 127, 361-404 C. Schochet (1996) The UCT, the Minor sequence, and canonical decomposition of Kasparon groups K-Theory 10, 49-72
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Splitting of extensions in the category of locally compact abelian groups