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On the descending central sequence of absolute Galois groups (2007

By Ido Efrat and Ján Mináč


Abstract. Let p be an odd prime number and F a field containing a primitive pth root of unity. We prove a new restriction on the group-theoretic structure of the absolute Galois group GF of F. Namely, the third subgroup G (3) F in the descending p-central sequence of GF is the intersection of all open normal subgroups N such that GF /N is 1, Z/p2, or the extra-special group Mp3 of order p 3 and exponent p 2. 1

Year: 2014
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