## $p$-central groups and Poincaré duality

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- by Thomas S. Weigel PDF
- Trans. Amer. Math. Soc.
**352**(2000), 4143-4154 Request permission

## 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 $\Lambda [x_{1},..,x_{n}]$.## References

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## Additional Information

**Thomas S. Weigel**- Affiliation: Math. Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, UK
- MR Author ID: 319262
- Email: weigel@maths.ox.ac.uk
- 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’.
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**352**(2000), 4143-4154 - MSC (1991): Primary 20J06
- DOI: https://doi.org/10.1090/S0002-9947-99-02385-5
- MathSciNet review: 1621710