On the cohomological characterization of real free pro-2-groups

The aim of this note is to give a cohomological characterization of the real free pro-2-groups. Thereal free pro-2-groups are the free pro-2-product of copies of ℤ/2ℤ with a free pro-2-group. They are characterized as the pro-2-groupsG for which there exists a character χ₀, whose kernel is a free pro-2-group, such that χ₀∪χ=χ∪χ, for every χ∈H ¹(G). We discuss the naturalness of these conditions and we state some relations between them and field arithmetic properties. Supported by a grant from CNPq-Brasil. This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag.