共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
Leila Schneps 《Israel Journal of Mathematics》1996,93(1):125-144
LetG be a finite group of even order, having a central element of order 2 which we denote by −1. IfG is a 2-group, letG be a maximal subgroup ofG containing −1, otherwise letG be a 2-Sylow subgroup ofG. LetH=G/{±1} andH=G/{±1}. Suppose there exists a regular extensionL
1 of ℚ(T) with Galois groupG. LetL be the subfield ofL
1 fixed byH. We make the hypothesis thatL
1 admits a quadratic extensionL
2 which is Galois overL of Galois groupG. IfG is not a 2-group we show thatL
1 then admits a quadratic extension which is Galois over ℚ(T) of Galois groupG and which can be given explicitly in terms ofL
2. IfG is a 2-group, we show that there exists an element α ε ℚ(T) such thatL
1 admits a quadratic extension which is Galois over ℚ(T) of Galois groupG if and only if the cyclic algebra (L/ℚ(T).a) splits. As an application of these results we explicitly construct several 2-groups as Galois groups of regular extensions
of ℚ(T). 相似文献
3.
Akito Nomura 《manuscripta mathematica》1993,79(1):379-390
LetL/k be a finite Galois extension with Galois groupG, and
a group extension. We study the existence of the Galois extensionM/L/k such that the canonical projection Gal(M/k)→Gal(L/k) coincides with the given homomorphismj:E→G and thatM/L is unramified. 相似文献
4.
Let B be an Azumaya Galois extension or a DeMeyer-Kanzaki Galois extension with Galois group G. Equivalent conditions are given for a separable subextension of a Galois extension in the skew group ring B * G being an invariant subring of a subgroup of the Galois group G.AMS Subject Classification (2000): 16S35, 16W20. 相似文献
5.
Let G be any finite group and any class of fields. By we denote the minimal number of realizations of G as a Galois group over some field from the class . For G abelian and the class of algebraic extensions of ℚ we give an explicit formula for . Similarly we treat the case of an abelian p-group G and the class which is conjectured to be the class of all fields of characteristic ≠p for which the Galois group of the maximal p-extension is finitely generated. For non-abelian groups G we offer a variety of sporadic results.
Received: 27 October 1998 / Revised version: 3 February 1999 相似文献
6.
LetL be a finite Galois extension of a global fieldF. It is shown that if the Galois groupG=Gal(L/F) satisfies a certain condition, thenL is a maximal commutative subfield of someF-division algebra if and only if the intermediate field corresponding to the Frattini subgroup ofG is also a maximal commutative subfield of someF-division algebra. In particular this condition holds ifG is a supersolvable group.
The third author was supported in part by the NSF under Grant DMS 97-01253. 相似文献
7.
Akito Nomura 《Archiv der Mathematik》2008,90(6):501-510
For a finite l-group G, let ram
t
(G) denote the minimal integer such that G can be realized as the Galois group of a tamely ramified extension of Q ramified only at ram
t
(G) finite primes. We study the upper bound of ram
t
(G) and give an improvement of the result of Plans. We also give the best bound of ram
t
(G) for all 3-groups G of order less than or equal to 35.
Received: 14 September 2007 相似文献
8.
Jochen Koenigsmann 《manuscripta mathematica》1998,95(1):251-271
Letp be a prime >2, letF be a field of characteristic ≠p containing a primitivep-th root of unity and letG
F
(p) be the Galois group of the maximal Galois-p-extension ofF. Ifrk G
F
(p)≤4 thenG
F
(p) is a free pro-p product of metabelian groups orG
F
(p) is a Demuškin group of rank 4. 相似文献
9.
Patrik Lundström 《代数通讯》2013,41(12):4331-4341
Let L ? K be an infinite Galois field extension with the property that every finite Galois extension M ? K, where L ? M, has a self-dual normal basis. We prove a self-dual normal basis theorem for L ? K when char (K) ≠2. 相似文献
10.
Let L/K be an ℓ-cyclic extension with Galois group G of algebraic function fields over an algebraically closed field k of characteristic p ≠ ℓ. In this paper, the -module structure of the ℓ-torsion of the Jacobian associated to L is explicitly determined. 相似文献
11.
Jochen Koenigsmann 《manuscripta mathematica》1998,95(2):251-271
Let p be a prime > 2, let F be a field of characteristic ≠p containing a primitive p-th root of unity and let G
F
(p) be the Galois group of the maximal Galois-p-extension of F. If rk G
F
(p)≤ 4 then G
F
(p) is a free pro-p product of metabelian groups or G
F
(p) is a Demuškin group of rank 4.
Received: 3 September 1997 / Revised version: 3 October 1997 相似文献
12.
Roger Ware 《manuscripta mathematica》1998,96(3):275-280
Let F be a formally real field which admits no quaternionic Galois extension. The structure of the Witt ring and the maximal pro-2
Galois group of F are investigated.
Received: 3 July 1997 / Revised version: 2 February 1998 相似文献
13.
Günter Lettl 《Archiv der Mathematik》2006,87(6):530-538
An element r of a field L will be called finitely arithmetically fixed (f.a.f.) if there exists some finite subset A of L containing r such that every map f from A to L which behaves “like a homomorphism” on A, leaves r fixed. This notion will be generalized to a relative one for any field extension L/K, and several results describing the set of f.a.f. elements are obtained.
Received: 21 December 2005 相似文献
14.
Let K be a field and let G be a finite group. G is K-admissible if there exists a Galois extension L of K with G=Gal(L/K) such that L is a maximal subfield of a central K-division algebra. We characterize those number fields K such that H is K-admissible where H is any subgroup of SL(2, 5) which contains a S
2-group. The method also yields refinements and alternate proofs of some known results including the fact that A
5 is K-admissible for every number field K.Dedicated to Professor Jacques Tits on the occasion of his sixtieth birthdayThe first author was partly supported by NSF fellowship DMS-8601130; the second author was partly supported by NSF grant DMS-8806371. 相似文献
15.
Mark Kisin 《Mathematische Zeitschrift》2000,233(2):347-363
If is a a scheme of finite type over a local field F, and is a proper smooth family, then to each rational point one can assign an extension of the absolute Galois group of F by the geometric fundamental group G of the fibre . If F has uniformiser , and residue characteristic p, we show that the corresponding extension of the absolute Galois group of by the maximal prime to p quotient of G is locally constant in the -adic topology of . We give a similar result in the case of non-proper families, and families over -adic analytic spaces.
Received August 14, 1998 相似文献
16.
This paper proves a generalization of Shafarevich's Conjecture, for fields of Laurent series in two variables over an arbitrary field. This result says that the absolute Galois group GK of such a field K is quasi-free of rank equal to the cardinality of K, i.e. every non-trivial finite split embedding problem for GK has exactly proper solutions. We also strengthen a result of Pop and Haran-Jarden on the existence of proper regular solutions to split embedding problems for curves over large fields; our strengthening concerns integral models of curves, which are two-dimensional. 相似文献
17.
R. Gow has investigated the problem of determining classical polynomials with Galois group Am, the alternating group on m letters, in the case that m is even (odd m being previously handled in work of I. Schur). He showed that the generalized Laguerre polynomial Lm(m)(x), defined below, has Galois group Am provided m>2 is even and Lm(m)(x) is irreducible (and obtained irreducibility in some cases). In this paper, we establish that Lm(m)(x) is irreducible for almost all m (and, hence, has Galois group Am for almost all even m). 相似文献
18.
François Laubie 《manuscripta mathematica》1999,100(2):197-202
Let G be a p-adic Lie group and let K be a finite extension of the p-adic number field ℚ
p
. There are finitely many filtrations of G which could be ramification filtrations of totally ramified Galois extensions of K with Galois group G.
Received: 19 October 1998 相似文献
19.
LetA be an abelian variety defined over a number fieldK. LetL be a finite Galois extension ofK with Galois groupG and let III(A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups ofA overK and ofA overL. Assuming these groups are finite, we compute [III(A/L)
G
]/[III(A/K)] and [III(A/K)]/[N(III(A/L))], where [X] is the order of a finite abelian groupX. Especially, whenL is a quadratic extension ofK, we derive a simple formula relating [III(A/L)], [III(A/K)], and [III(A
x/K)] whereA
x is the twist ofA by the non-trivial characterχ ofG. 相似文献
20.
Mowaffaq Hajja 《代数通讯》2013,41(3):761-776
It is shown in [5, Theorem 3] that if s is an algebraic automorphism of a k-vector space V with minimalpolynomial μ(T) ∈ K[T], then the extension σ of s to a k-automorphism of the field of quotients of the symmetric k-algebra k(V) of V is completely determined by μ(T) (and dimkV). In Theorem 4 of this article, we show that σ is almost completely determined by the radical μ0(T) of μ(T) and we see in particular that if μ(T) is separable then the rationality of (the fixed field of) σ depends only on μ0(T). In Theorem 5, the rationality of σ is established under certain assumptions on the Galois group of μ0(T). 相似文献