On the descending central sequence of absolute Galois groups

Ido Efrat; Ján Mináč

doi:10.1353/ajm.2011.0041

On the descending central sequence of absolute Galois groups

Ido Efrat, Ján Mináč

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

40 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 G_F of F. Namely, the third subgroup G⁽³⁾_F 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/p², or the extra-special group M_p3 of order p³ and exponent p².

Original language	English
Pages (from-to)	1503-1532
Number of pages	30
Journal	American Journal of Mathematics
Volume	133
Issue number	6
DOIs	https://doi.org/10.1353/ajm.2011.0041
State	Published - 1 Dec 2011

ASJC Scopus subject areas

General Mathematics

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10.1353/ajm.2011.0041

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title = "On the descending central sequence of absolute Galois groups",

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.",

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AB - 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.

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On the descending central sequence of absolute Galois groups

Abstract

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