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Roots and Wreath Products

Published online by Cambridge University Press:  24 October 2008

Gilbert Baumslag
Gilbert Baumslag
Affiliation:
Department of MathematicsThe UniversityManchester 13 Fine Hall Princeton
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Extract

B. H. Neumann (5) has shown, by using free products with an amalgamated subgroup, that every group can be embedded in a divisible group. This theorem can also be proved, in an entirely different way, by making use of the wreath product (Baumslag(1)). In view of this connexion between roots in groups and the wreath product, a study is made here of the conditions which ensure that the wreath product (and also the unrestricted wreath product) shares certain properties regarding the existence and uniqueness of roots with the groups from which it is composed.

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 2 , April 1960 , pp. 109 - 117
Copyright
Copyright © Cambridge Philosophical Society 1960

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References

REFERENCES

(1)Baumslag, G., Wreath products and p-groups. Proc. Camb. Phil. Soc. 55 (1959), 224–31.CrossRefGoogle Scholar
(2)Baumslag, G., Groups with unique roots. Acta Math. to be published.Google Scholar
(3)Hall, P., Finiteness conditions for soluble groups. Proc. Lond. Math. Soc. (3), 4 (1954), 419–36.Google Scholar
(4)Kuroš, A. G., Theory of groups, vol. 2 (New York,1956).Google Scholar
(5)Neumann, B. H., Adjunction of elements to groups. J. Lond. Math. Soc. 18 (1943), 12–20.Google Scholar