-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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we investigate the mod cohomology ring of finite -central groups with a certain extension property. For odd it turns out that the structure of the cohomology ring characterizes this class of groups up to extensions by -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--group of rank is isomorphic to .

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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