𝑝-central groups and Poincaré duality

Weigel, Thomas

doi:10.1090/S0002-9947-99-02385-5

$p$-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 $\Lambda [x_{1},..,x_{n}]$.

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