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On prosolvable subgroups of profinite free products and some applications

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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.

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References

  • [BNW] Binz, E.— Neukirch, J.— Wenzel, G.G. A subgroup theorem for free product of profinite groups, J. of Algebra19 (1971), 104–109

    Article  MathSciNet  Google Scholar 

  • [H1] Haran, D. On closed subgroups of free products of profinite groups, Proc. London Math. Soc.55 (1987), 266–289

    MathSciNet  Google Scholar 

  • [H2] Haran, D. Private communication, October 1990.

  • [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.

    MathSciNet  Google Scholar 

  • [HJ2] Haran, D.— Jarden, M. The absolute Galois group of a pseudop-adically closed field, J. reine angew. Math.383 (1988), 147–206

    MathSciNet  Google Scholar 

  • [HR] Herfort, W.— Ribes, L. Torsion elements and centralizers in free products of profinite groups, J. reine angew. Math.358 (1985), 155–161

    MathSciNet  Google Scholar 

  • [H] Huppert, B. Endliche Gruppen I, Springer-Verlag Berlin Heidelberg New York 1967

    MATH  Google Scholar 

  • [J] Jarden, M. Prosolvable subgroups of free products of profinite groups, Communications in Alg.22 Vol. 4 (1994), 1467–1494

    MathSciNet  Google Scholar 

  • [N] Neukirch, J. Über eine algebraische Kennzeichnung der Henselkörper, J. reine angew. Math.231 (1968), 75–81

    MathSciNet  Google Scholar 

  • [P1] Pop, F. Classically projective groups and pseudo classically closed fields, Preprint, Heidelberg, 1990

  • [P2] Pop, F. On Grothendieck's conjecture of birational anabelian geometry, Ann. of Math.,138 (1994), 145–182

    Article  MathSciNet  Google Scholar 

  • [R] Roquette, P. Some tendences in contemporary algebra, in: Perspectives in Mathematics, Anniversary of Oberwolfach 1984, Basel 1984, 393–422

  • [S] Serre, J. P. Cohomologie galoisienne, LNM 5, Springer Verlag 1973

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  1. Mathematisches Institut der Universität, Im Neuenheimer Feld 288, D-6900, Heidelberg

    Florian Pop

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  1. Florian Pop
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This article was processed by the author using the Springer-Verlag TEX mamath macro package 1990.

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Pop, F. On prosolvable subgroups of profinite free products and some applications. Manuscripta Math 86, 125–135 (1995). https://doi.org/10.1007/BF02567982

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