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Subgroups of free pro-p-products

Published online by Cambridge University Press:  24 October 2008

Wolfgang Herfort  and
Luis Ribes
Wolfgang Herfort
Affiliation:
Institut für Numerische und Angewandte Mathematik, Technische Universität Wien, Austria
Luis Ribes
Affiliation:
Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada
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Extract

If F is a free profinite group, it is well known that the closed subgroups of F need not be free profinite; however, if p is a prime number, every closed subgroup of a free pro-p-group is free pio-p (cf. [2, 8, 7]). In this paper we show that there is an analogous contrast regarding the closed subgroups of free products in the category of profinite groups, and the closed subgroups of free products in the category of pro-p-groups, at least for (topologically) finitely generated subgroups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 2 , March 1987 , pp. 197 - 206
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

[1]Binz, E., Neukirch, J. and Wenzel, G. H.. A subgroup theorem for free products of profinite groups. J. Algebra 19 (1971), 104–109.CrossRefGoogle Scholar
[2]Douady, A.. Cohomologie des groupes compacts totalment discontinus. Séminaire Bourbaki. exposé 189 (1959–1960).Google Scholar
[3]Gildenhuys, D. and Ribes, L.. A Kurosh subgroup theorem for free pro- products of pro--groups. Trans. Amer. Math. Soc. 186 (1973), 309–329.Google Scholar
[4]Gildenhuys, D. and Ribes, L.. Profinite groups and Boolean graphs. J. Pure Appl. Algebra 12 (1978), 21–47.CrossRefGoogle Scholar
[5]Herfort, W. and Ribes, L.. Torsion elements and centralizers in free products of profinite groups. J. Reine Angew. Math. 358 (1985), 155–161.Google Scholar
[6]Lubotzky, A.. Combinatorial group theory for pro-p-groups. J. Pure Appl. Algebra 25 (1982), 311–325.CrossRefGoogle Scholar
[7]Ribes, L.. Introduction to profinite groups and Galois cohomology. Queen's Papers in Pure Appl. Math., no. 24 (Kingston, 1970).Google Scholar
[8]Serre, J.-P.. Cohomologie galoisienne. Lecture Notes in Math. vol. 5 (Springer-Verlag, 1965).CrossRefGoogle Scholar