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$p$-central groups and Poincaré duality


Author: Thomas S. Weigel
Journal: Trans. Amer. Math. Soc. 352 (2000), 4143-4154
MSC (1991): Primary 20J06
DOI: https://doi.org/10.1090/S0002-9947-99-02385-5
Published electronically: May 3, 1999
MathSciNet review: 1621710
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Abstract: In this note we investigate the mod $p$ cohomology ring of finite $p$-central groups with a certain extension property. For $p$ odd it turns out that the structure of the cohomology ring characterizes this class of groups up to extensions by $p'$-groups. For certain examples the cohomology ring can be calculated explicitly. As a by-product one gets an alternative proof of a theorem of M.Lazard which states that the Galois cohomology of a uniformly powerful pro-$p$-group of rank $n$ is isomorphic to $\Lambda [x_{1},..,x_{n}]$.


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Additional Information

Thomas S. Weigel
Affiliation: Math. Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, UK
Email: weigel@maths.ox.ac.uk

DOI: https://doi.org/10.1090/S0002-9947-99-02385-5
Received by editor(s): February 12, 1997
Received by editor(s) in revised form: March 28, 1998
Published electronically: May 3, 1999
Additional Notes: The author gratefully acknowledges financial support of the ‘Deutsche Forschungsgemeinschaft’ through a ‘Heisenberg Stipendium’.
Article copyright: © Copyright 2000 American Mathematical Society

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