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Transactions of the American Mathematical Society

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Free products of topological groups with central amalgamation. I


Authors: M. S. Khan and Sidney A. Morris
Journal: Trans. Amer. Math. Soc. 273 (1982), 405-416
MSC: Primary 22A05; Secondary 20E06, 54D50
DOI: https://doi.org/10.1090/S0002-9947-1982-0667153-5
MathSciNet review: 667153
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Abstract: It is proved that the amalgamated free product of any two Hausdorff topological groups exists and is Hausdorff, providing the subgroup which is being amalgamated is closed and central.


References [Enhancements On Off] (What's this?)

  • [1] D. B. A. Epstein, A result on free products with amalgamation, J. London Math. Soc. 37 (1962), 130-132. MR 0137752 (25:1201)
  • [2] M. I. Graev, Free topological groups, Izv. Akad. Nauk SSSR Ser. Mat. 12 (1948), 279-324; English transl., Amer. Math. Soc. Transl. No. 35 (1951). Reprint Amer. Math. Soc. Transl. (1) No. 8 (1962), 305-364.
  • [3] -, On free products of topological groups, Izv. Akad. Nauk SSSR Ser. Mat. 14 (1950), 343-354. (Russian). MR 0036768 (12:158c)
  • [4] M. S. Khan and Sidney A. Morris, Amalgamated direct products of topological groups, Math. Chronicle (to appear). MR 677451 (84a:22004)
  • [5] Wilhelm Magnus, Abraham Karrass and Donald Solitar, Combinatorial group theory, Dover, New York, 1976. MR 0422434 (54:10423)
  • [6] B. H. Neumann, An essay on free products of groups with amalgamations, Philos. Trans. Roy. Soc. London Ser. A 246 (1954), 503-554. MR 0062741 (16:10d)
  • [7] Edward T. Ordman, Free products of topological groups with equal uniformities. I, II, Colloq. Math. 31 (1974), 37-43; 45-49. MR 0374319 (51:10519)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1982-0667153-5
Article copyright: © Copyright 1982 American Mathematical Society

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