Finitely generated pro-p Galois groups of p-Henselian fields
نویسندگان
چکیده
منابع مشابه
On the verbal width of finitely generated pro-p groups
Let p be a prime. It is proved that a non-trivial word w from a free group F has finite width in every finitely generated pro-p group if and only if w 6∈ (F ′)pF ′′. Also it is shown that any word w has finite width in a compact p-adic group.
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Let p be a prime. It is a fundamental problem to classify the absolute Galois groups GF of fields F containing a primitive pth root of unity ξp. In this paper we present several constraints on such GF , using restrictions on the cohomology of index p normal subgroups from [LMS]. In section 1 we classify all maximal p-elementary abelian-by-order p quotients of these GF . In the case p > 2, each ...
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In (Arch. Math. 57 (1991), pp. 446–455), R. Farré proved a positivstellensatz for real-series closed fields. Here we consider p-valued fields 〈K, vp〉 with a non-trivial valuation v which satisfies a compatibility condition between vp and v. We use this notion to establish the p-adic analogue of real-series closed fields; these fields are called henselian residually p-adically closed fields. Fir...
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Fix a prime p, a number field K, and a finite set S of places of K none of which has residue characteristic p. Fix an algebraic closure K of K and let KS be the maximal p-extension of K inside K which is unramified outside S; it is the compositum of all finite p-power degree extensions of K unramified outside S. We assume that real places of K not contained in S do not complexify in the extensi...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1999
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(98)00033-4