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)]
Weigel, T. (2000). p-central groups and Poincare duality. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 352(9), 4143-4154 [10.1090/S0002-9947-99-02385-5].
p-central groups and Poincare duality
Weigel, TS
2000
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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