Abstract
We consider the p-Zassenhaus filtration (Gn) of a profinite group G. Suppose that G=S/N for a free profinite group S and a normal subgroup N of S contained in Sn. Under a cohomological assumption on the n-fold Massey products (which holds, e.g., if G has p-cohomological dimension ≤ 1), we prove that Gn+1 is the intersection of all kernels of upper-triangular unipotent (n+1)-dimensional representations of G over Fp. This extends earlier results by Mináč, Spira, and the author on the structure of absolute Galois groups of fields.
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