On the descending central sequence of absolute Galois groups

Ido Efrat, Ján Mináč

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31 Scopus citations

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 p3 and exponent p2.

Original languageEnglish
Pages (from-to)1503-1532
Number of pages30
JournalAmerican Journal of Mathematics
Volume133
Issue number6
DOIs
StatePublished - 1 Dec 2011

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