Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T14:56:25.776Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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