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Certain subgroups of free products

Published online by Cambridge University Press:  26 February 2010

D. E. Cohen
D. E. Cohen
Affiliation:
Birmingham University.
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Extract

Let G1,… Gn be groups, let *Gi be their free product, and let ´ Gi be their direct product. A homomorphism may be defined by requiring it to be trivial on Gj and the identity on Gi for i ¹ j. Let [G1 … Gn] = Çker pj. P. J. Hilton [2] proves that [G1, …, Gn] is a free group, and, if HiÌGi, i = 1, …, n, that [H1,… Hn] is a free factor of [G1 … Gn]. He asks whether, if Hλi Ì Gi, λ = 1, …, k, i = 1, …, n, and Hλ = [Hλ1, …, Hλn] the group generated by the Hλ is a free factor of [G1, …, Gn].

Type
Research Article
Information
Mathematika , Volume 7 , Issue 2 , December 1960 , pp. 117 - 124
Copyright
Copyright © University College London 1960

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References

011.Gruenberg, K. W., “Residual properties of infinite soluble groups”, Proc. London Math. Soc. (3), 7 (1957), 29–62.CrossRefGoogle Scholar
2.Hilton, P. J., “Remark on free products of groups”, Trans. Amer. Math. Soc. (to appear).Google Scholar
3.Weir, A. J., “The Reidemeister-Schreier and Kuroš subgroup theorems”, Mathematika, 3 (1956), 47–55.CrossRefGoogle Scholar