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Extensions of pro-p groups of cohomological dimension two

Published online by Cambridge University Press:  24 October 2008

Tilmann Würfel
Tilmann Würfel
Affiliation:
Pennsylvania State University, Wilkes-Barre Campus, Lehman, PA 18627, U.S.A.
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Extract

The purpose of this note is to extend Brumer's characterization of pro-p groups of cohomological dimension two ([1], corollary 5·3) to presentations more general than free ones. The result is then used to rid a proof in [7] of certain field theoretic ingredients. As a by-product we complete a result of Tsvetkov [6] about group extensions obtained by omitting relations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 2 , March 1986 , pp. 209 - 211
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Brumer, A.. Pseudocompact algebras, profinite groups, and class formations. J. Algebra 4 (1966), 442–470.Google Scholar
[2]Labute, J. P.. Demuškin groups of rank ℵ0. Bull. Soc. Math. France 94 (1966), 211–244.CrossRefGoogle Scholar
[3]Merkur'ev, A. S. and Suslin, A. A.. K-cohomology of Severi-Brauer varieties and the norm residue homomorphism. Math. USSR-Izv. 21 (1983), 307–340.CrossRefGoogle Scholar
[4]Neukirch, J.. Freie Produkte proendlicher Gruppen und ihre Kohomologie. Arch. Math. 22 (1971), 337–357.Google Scholar
[5]Shatz, S. S.. Profinite Groups, Arithmetic, and Geometry. Annals of Mathematics Studies no. 67 (Princeton University Press, 1972).CrossRefGoogle Scholar
[6]Tsvetkov, V. M.. On pro-p groups of cohomological dimension two. Soviet Math. Dokl. 28 (1983), 285–289.Google Scholar
[7]Würfel, T.. A remark on the structure of absolute Galois groups. Proc. Amer. Math. Soc. (in press).Google Scholar