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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] G. Baumslag, Wreath products and $ p$-groups, Proc. Cambridge Philos. Soc. 55 (1959), 224-231. MR 0105437 (21:4179)
  • [2] -, Some aspects of groups with unique roots, Acta Math. 104 (1960), 217-303. MR 0122859 (23:A191)
  • [3] P. Hilton, On direct limits of nilpotent groups, Lecture Notes in Math., vol. 418, Springer-Verlag, Berlin, Heidelberg and New York, 1974, pp. 68-77. 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] -, 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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Article copyright: © Copyright 1988 American Mathematical Society

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