On the descending central sequence of absolute Galois groups
نویسندگان
چکیده
منابع مشابه
On the Descending Central Sequence of Absolute Galois Groups
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/p , or the extra-special group Mp3 of order p and exponent p.
متن کاملOn the Descending Central Sequence of Absolute Galois Groups
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/p , or the modular group Mp3 of order p .
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Let $G$ be a finite group. The automorphism $sigma$ of a group $G$ is said to be an absolute central automorphism, if for all $xin G$, $x^{-1}x^{sigma}in L(G)$, where $L(G)$ be the absolute centre of $G$. In this paper, we study some properties of absolute central automorphisms of a given finite $p$-group.
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If the absolute Galois group GK of a field K is a direct product GK = G1 × G2 then one of the factors is prosolvable and either G1 and G2 have coprime order or K is henselian and the direct product decomposition reflects the ramification structure of GK . So, typically, the direct product of two absolute Galois groups is not an absolute Galois group. In contrast, free (profinite) products of ab...
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Let k be an algebraically closed field of characteristic zero, L its finitely generated extension of transcendence degree ≥ 2, and L another finitely generated extension of k. It is a result of Bogomolov [B2] that any isomorphism between Gal(L/L) and Gal(L′/L) is induced by an isomorphism of fields L −→ L′ identifying L with L. If the transcendence degree of L over k is one, the group Gal(L/L) ...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2011
ISSN: 1080-6377
DOI: 10.1353/ajm.2011.0041