Demuskin groups, Galois modules, and the elementary type conjecture.-

Publication Type:

Journal Article

Source:

J. Algebra, Volume 304, Issue 206, p.1130-1146 (2006)

URL:

http://www.math.mcgill.ca/labute/papers/LLMS2.pdf

Abstract:

Let p be a prime and F(p) the maximal p-extension of a field F containing a primitive p-th root of unity. We give a new characterization of Demuˇskin groups among Galois groups Gal(F(p)=F) when p = 2, and, assuming the Elementary Type Conjecture, when p > 2 as well. This characterization is in terms of the structure, as Galois modules, of the Galois cohomology of index p subgroups of Gal(F(p)=F).

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