Pure extensions of locally compact abelian groups

Peter Loth

Rendiconti del Seminario Matematico della Università di Padova (2006)

  • Volume: 116, page 31-40
  • ISSN: 0041-8994

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Loth, Peter. "Pure extensions of locally compact abelian groups." Rendiconti del Seminario Matematico della Università di Padova 116 (2006): 31-40. <http://eudml.org/doc/108700>.

@article{Loth2006,
author = {Loth, Peter},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {31-40},
publisher = {Seminario Matematico of the University of Padua},
title = {Pure extensions of locally compact abelian groups},
url = {http://eudml.org/doc/108700},
volume = {116},
year = {2006},
}

TY - JOUR
AU - Loth, Peter
TI - Pure extensions of locally compact abelian groups
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2006
PB - Seminario Matematico of the University of Padua
VL - 116
SP - 31
EP - 40
LA - eng
UR - http://eudml.org/doc/108700
ER -

References

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  1. [AA] D. L. ARMACOST and W. L. ARMACOST, Uniqueness in structure theorems for LCA groups, Can. J. Math. 30 (1978), pp. 593-599. Zbl0358.22001MR578649
  2. [A] D. L. ARMACOST, The Structure of Locally Compact Abelian Groups, Marcel Dekker Inc., New York, 1981. Zbl0509.22003MR637201
  3. [B] J. BRACONNIER, Sur les groupes topologiques localement compacts, J. Math. Pures Appl., N.S. 27 (1948), pp. 1-85. Zbl0034.16401MR25473
  4. [F] L. FUCHS, Infinite Abelian Groups, Vol. I, Academic Press, New York, 1970. Zbl0209.05503MR255673
  5. [Fu1] R. O. FULP, Homological study of purity in locally compact groups, Proc. London Math. Soc. 21 (1970), pp. 501-512. Zbl0222.22004MR279229
  6. [Fu2] R. O. FULP, Splitting locally compact abelian groups, Michigan Math. J. 19 (1972), pp. 47-55. Zbl0229.22005MR294559
  7. [FG1] R. O. FULP and P. GRIFFITH, Extensions of locally compact abelian groups I, Trans. Amer. Math. Soc. 154 (1971), pp. 341-356. Zbl0216.34302MR272870
  8. [FG2] R. O. FULP and P. GRIFFITH, Extensions of locally compact abelian groups II, Trans. Amer. Math. Soc. 154 (1971), pp. 357-363. Zbl0216.34302MR272870
  9. [HH] S. HARTMAN and A. HULANICKI, Les sous-groupes purs et leurs duals, Fund. Math. 45 (1957), pp. 71-77. Zbl0083.25501MR92102
  10. [HR] E. HEWITT and K. ROSS, Abstract Harmonic Analysis, Vol. I, Second Edition, Springer Verlag, Berlin, 1979. Zbl0416.43001MR551496
  11. [K] I. KAPLANSKY, Infinite Abelian Groups, Revised Edition, Univ. of Michigan Press, Ann Arbor, Michigan, 1969. Zbl0194.04402MR233887
  12. [Kh] J. A. KHAN, The finite torsion subgroup of an LCA group need not split, Period. Math. Hungar. 31 (1995), pp. 43-44. Zbl0845.22005MR1349292
  13. [L1] P. LOTH, Topologically pure extensions, Abelian Groups, Rings and Modules, Proceedings of the AGRAM 2000 Conference in Perth, Western Australia, July 9-15, 2000, Contemporary Mathematics 273, American Mathematical Society (2001), pp. 191-201. Zbl0980.22007MR1817162
  14. [L2] P. LOTH, On pure subgroups of locally compact abelian groups, Arch. Math. 81, (2003), pp. 255-257. Zbl1037.22006MR2013255
  15. [M] M. MOSKOWITZ, Homological algebra in locally compact abelian groups, Trans. Amer. Math. Soc. 127 (1967), pp. 361-404. Zbl0149.26302MR215016
  16. [R] L. C. ROBERTSON, Connectivity, divisibility and torsion, Trans. Amer. Math. Soc. 128 (1967), pp. 482-505. Zbl0153.04401MR217211
  17. [V] N. VILENKIN, Direct decompositions of topological groups I, Mat. Sb., N. S. 19 (61) (1946), pp. 85-154. [English translation from the Russian by E. Hewitt in A.M.S. Translations, Series 1, Volume 23, Providence, Rhode Island (1950).] Zbl0061.04302MR17283

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