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Maximal abelian subgroups of free profinite groups

Published online by Cambridge University Press:  24 October 2008

Dan Haran  and
Alexander Lubotzky
Dan Haran
Affiliation:
Mathematisches Institut, Universität Erlangen, West Germany
Alexander Lubotzky
Affiliation:
Institute of Mathematics, The Hebrew University, Jersualem, Israel
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Extract

The aim of this note is to answer in the negative a question of W. -D. Geyer, asked at the 1983 Group Theory Meeting in Oberwolfach: Is a maximal abelian subgroup A of a free profinite group F necessarily isomorphic to , the profinite completion of

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 1 , January 1985 , pp. 51 - 55
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Ax, J.. A metamathematical approach to some problems in number theory. Proc. of Symposia in Pure Math. vol. 20 (1971), 161–190. American Mathematical Society.CrossRefGoogle Scholar
[2]Geyer, W.-D.. Unendliche algebraische Zahlkörper, über denen jede Gleichung auflösbar von beschränkter Stufe ist. J. Number Theory 1 (1969), 346–374.CrossRefGoogle Scholar
[3]Geyer, W.-D.. Galois groups of intersections of local fields. Israel J. Math. 30 (1978), 382–396.CrossRefGoogle Scholar
[4]Lubotzky, A. and Dries, L. van den. Subgroups of free pro-finite groups and large subfields of . Israel J. Math. 39 (1981), 25–45.CrossRefGoogle Scholar
[5]Lyndon, R. C. and Schupp, P. E.. Combinatorial Group Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete 89 (Springer-Verlag, 1977).Google Scholar
[6]Neukirch, J.. Freie Produkte proendlicher Gruppen und ihre Kohomologie. Arch. Math. 22 (1971), 337–357.CrossRefGoogle Scholar
[7]Scott, P.. Subgroups of surface groups are almost geometric. J. London Math. Soc. 17 (1978), 555–565.CrossRefGoogle Scholar
[8]Ribes, L.. Introduction to profinite groups and Galois cohomology. Queens Papers in Pure and Applied Mathematics, vol. 24 (Kingston).Google Scholar