Ido Efrat and Jan Minac: On the descending central sequence of absolute Galois groups,

Submission: 2009, Sep 25

Let p be an odd prime number and F a field containing a primitive p-th root of unity. We prove a new restriction on the group-theoretic structure of the absolute Galois group G_F of F. Namely, the third subgroup G_F^{(3)} in the descending p-central sequence of G_F is the intersection of all open normal subgroups N such that G_F/N is 1, Z/p^2, or the extra-special group of order p^3 and exponent p^2.

2000 Mathematics Subject Classification: 12F10, 12G05, 12E30

Keywords and Phrases: descending central sequence, absolute Galois group, Galois cohomology, embedding problem, W-group, Bockstein map

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