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, Volume 86, Issue 1, pp 125–135 | Cite as

On prosolvable subgroups of profinite free products and some applications

  • Florian Pop
Article
Received:

Abstract

In this paper we give a discription of “large” prosolvable subgroups of profinite free products. Based on this result and a result of Herfort-Ribes we show that under quite general hypothesis on the obstruction set relatively projective groups are in fact strongly relatively projective. This in turn is one of the main steps in solving the inverseabsolute Galois problem for such groups.

Keywords

Prime Number Projective Group Canonical Projection Closed Subgroup Open Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. [BNW] Binz, E.— Neukirch, J.— Wenzel, G.G. A subgroup theorem for free product of profinite groups, J. of Algebra19 (1971), 104–109CrossRefMathSciNetGoogle Scholar
  2. [H1] Haran, D. On closed subgroups of free products of profinite groups, Proc. London Math. Soc.55 (1987), 266–289MathSciNetGoogle Scholar
  3. [H2] Haran, D. Private communication, October 1990.Google Scholar
  4. [HJ1] Haran, D.— Jarden, M. The absolute Galois group of a pseudo real closed field, Ann. Scuola Norm. Sup. Pisa, Serie IV,12 (1985), 449–489.MathSciNetGoogle Scholar
  5. [HJ2] Haran, D.— Jarden, M. The absolute Galois group of a pseudop-adically closed field, J. reine angew. Math.383 (1988), 147–206MathSciNetGoogle Scholar
  6. [HR] Herfort, W.— Ribes, L. Torsion elements and centralizers in free products of profinite groups, J. reine angew. Math.358 (1985), 155–161MathSciNetGoogle Scholar
  7. [H] Huppert, B. Endliche Gruppen I, Springer-Verlag Berlin Heidelberg New York 1967MATHGoogle Scholar
  8. [J] Jarden, M. Prosolvable subgroups of free products of profinite groups, Communications in Alg.22 Vol. 4 (1994), 1467–1494MathSciNetGoogle Scholar
  9. [N] Neukirch, J. Über eine algebraische Kennzeichnung der Henselkörper, J. reine angew. Math.231 (1968), 75–81MathSciNetGoogle Scholar
  10. [P1] Pop, F. Classically projective groups and pseudo classically closed fields, Preprint, Heidelberg, 1990Google Scholar
  11. [P2] Pop, F. On Grothendieck's conjecture of birational anabelian geometry, Ann. of Math.,138 (1994), 145–182CrossRefMathSciNetGoogle Scholar
  12. [R] Roquette, P. Some tendences in contemporary algebra, in: Perspectives in Mathematics, Anniversary of Oberwolfach 1984, Basel 1984, 393–422Google Scholar
  13. [S] Serre, J. P. Cohomologie galoisienne, LNM 5, Springer Verlag 1973Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Florian Pop
    • 1
  1. 1.Mathematisches Institut der UniversitätHeidelberg

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