Subject: comment on N.Kuhn remark From: Alejandro Adem Date: Fri, 11 Feb 2005 14:12:42 -0800 (PST) To: dmd1@lehigh.edu This comment is about a construction Nick Kuhn recently mentioned: ------------------------------ Let V be a finite dimensional Z/2 vector space (and let homology and cohomology have Z/2 coefficients). There is a `universal' central group extension H_2(V) --> G(V) --> V whose d_2 differential in the Serre spectral sequence for H^*(G(V)) is an isomorphism from H2(V)=E_2^{0,1} to E_2^{2,0}=H2(V). -------------- The groups described by Nick are known as universal W-groups, and have been studied by Minac and Spira in applications to Galois cohomology. Calculating their mod 2 cohomology is an interesting open problem (see math.AT/9812169). The mod p analogues have also been studied; their cohomology can be completely computed if p is large enough with respect to the dimension of V (see math.AT/0008229). And yes, they are pC groups. Alejandro Adem.