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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Embedding of $ U\sb \omega$-groups in $ D\sb \omega$-groups


Author: Charles Cassidy
Journal: Proc. Amer. Math. Soc. 103 (1988), 15-20
MSC: Primary 20E06; Secondary 20E25
MathSciNet review: 938636
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Abstract: The purpose of this paper is to give certain new conditions under which it is possible to show that a group in which the equation $ {x^p} = a$ has at most one solution for every $ a$, can be embedded in another group in which the equation $ {x^p} = a$ has exactly one solution for every $ a$.

It has been known for a long time that locally nilpotent groups satisfy the above property but some other sufficient conditions have also been found by G. Baumslag in his thesis. Conditions related to Baumslag's are examined.


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

  • [1] Gilbert Baumslag, Wreath products and 𝑝-groups, Proc. Cambridge Philos. Soc. 55 (1959), 224–231. MR 0105437 (21 #4179)
  • [2] Gilbert Baumslag, Some aspects of groups with unique roots, Acta Math. 104 (1960), 217–303. MR 0122859 (23 #A191)
  • [3] Peter Hilton, On direct limits of nilpotent groups, Localization in group theory and homotopy theory, and related topics (Sympos., Battelle Seattle Res. Center, Seattle, Wash., 1974) Springer, Berlin, 1974, pp. 68–77. Lecture Notes in Math., Vol. 418. MR 0382446 (52 #3329)
  • [4] B. H. Neumann, Adjunction of elements to groups, J. London Math. Soc. 18 (1943), 4–11. MR 0008808 (5,58s)
  • [5] 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)
  • [6] P. Ribenboim, Equations in groups, with special emphasis on localization and torsion, Queen's Preprint 1982-22, Kingston, Ontario, Canada.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0938636-6
PII: S 0002-9939(1988)0938636-6
Article copyright: © Copyright 1988 American Mathematical Society