A recursive description of pro-p Galois groups
نویسندگان
چکیده
منابع مشابه
Computing Pro-P Galois Groups
We describe methods for explicit computation of Galois groups of certain tamely ramified p-extensions. In the finite case this yields a short list of candidates for the Galois group. In the infinite case it produces a family or few families of likely candidates.
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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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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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In this article we introduce a heuristic prediction for the distribution of the isomorphism class of GS(p), the Galois group of the maximal pro-p extension of Q unramified outside of S, where S is a ”random” set of primes. That these groups should exhibit any statistical regularity is not at all obvious; our expectations in this direction are guided by the Cohen-Lenstra conjectures, which (amon...
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The smallest non-abelian p-groups play a fundamental role in the theory of Galois p-extensions. We illustrate this by highlighting their role in the definition of the norm residue map in Galois cohomology. We then determine how often these groups — as well as other closely related, larger p-groups — occur as Galois groups over given base fields. We show further how the appearance of some Galois...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2003.12.014