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1.
利用Galois理论,研究了4次根式扩张的一些性质.利用这些性质,给出了域扩张是4次根式扩张的一些等价条件,证明了域扩张是4次根式扩张当且仅当域扩张是4次Galois扩张且Galois群是4阶循环群.  相似文献   

2.
童丽珍 《数学杂志》2005,25(2):123-129
本文研究了关于Γ-右等价和Γ-左-右等价的Γ-等变分歧问题,利用了奇点理论和紧群表示论,获得了判别这类问题的一些准则,并推广了文[3]的一些结果.  相似文献   

3.
对二阶多项式系统通过建立相对微分Galois群的概念,给出保形相对微分Galois群与M(o)bius变换子群的关系,并证明如果系统的一个保形相对微分Galois群的SL(2,C)表示是导出长度不超过2的可解群,该系统一定在Liouville意义下可积.顺便补上第一作者1996年在本刊发表的论文中的一个遗漏.  相似文献   

4.
对二阶多项式系统通过建立相对微分Galois群的概念,给出保形相对微分Galois群与Möbius变换子群的关系, 并证明如果系统的一个保形相对微分Galois群的SL(2,C)表示是导出长度不超过2的可解群, 该系统一定在Liouville意义下可积. 顺便补上第一作者1996年在本刊发表的论文中的一个遗漏.  相似文献   

5.
周柏荣 《数学学报》1991,34(2):186-190
本文发展了群Miyashita作用,并在非交换环情形给出域论及Galois理论中Artin引理,即环A作为其中心子环R上的模的生成元个数与Galois群Gal(A/R)的关系。  相似文献   

6.
樊恽 《中国科学A辑》1991,34(4):355-364
本文对特征P的基域F引入适当的Galois群T,讨论p置换模的Green环的Conlon比析在Galois群T作用下的动态,证明了在T作用下p置换模的Green环的不动点集重合于置换模的Green环。  相似文献   

7.
本文研究一类特殊Gross曲线的算术性质,建立Selmer群以及增大的Selmer群和域扩张的Galois群之间的联系,并刻画了曲线在局部域上有理点的部分结构信息.  相似文献   

8.
对二阶多项式系统通过建立相对微分Galois群的概念,给出保形相对微分Galois群与Mobius变换子群的关系,并证明如果系统的一个保形相对微分Galois群的SL(2,C)表示是导出长度不超过2的可解群,该系统一定在Liouville意义下可积.顺便补上第一作者1996年在本刊发表的论文中的一个遗漏.  相似文献   

9.
将形式化方法引入到Galois联络的研究当中,提出了一种基于Galois联络的逻辑系统LGC,给出了其等价形式并证明了完备性定理.由于Galois联络与粗糙集及概念格有着紧密的联系,故本文的结果对概念格及粗糙集的形式化研究有一定的启示作用.  相似文献   

10.
张习勇  郭华 《数学学报》2008,51(5):911-922
利用Galois环、Bent函数、Gaolis环上的部分指数和等技巧,构造了指数不超过4的有限交换群上的分裂型相对差集和一类非分裂型组合集.  相似文献   

11.
The combinatorial classification of plane trees by the number of realizations of their valency sets has distinguished some special classes of plane trees. One of them, the plane trees of diameter 4, turned out to be a very interesting object of investigation from the Galois action point of view. In this paper, we present equation sets for some subclasses of trees of diameter 4, calculate discriminants of the corresponding generalized Chebyshev polynomials, some related polynomials, and their fields of definitions, and use this to get some information about the Galois action on plane trees. Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 6, pp. 19–33, 2007.  相似文献   

12.
《Discrete Mathematics》2023,346(1):113167
Galois inner product is a generalization of the Euclidean inner product and Hermitian inner product. The theory on linear codes under Galois inner product can be applied in the constructions of MDS codes and quantum error-correcting codes. In this paper, we construct Galois self-dual codes and MDS Galois self-dual codes from extensions of constacyclic codes. First, we explicitly determine all the Type II splittings leading to all the Type II duadic constacyclic codes in two cases. Second, we propose methods to extend two classes of constacyclic codes to obtain Galois self-dual codes, and we also provide existence conditions of Galois self-dual codes which are extensions of constacyclic codes. Finally, we construct some (almost) MDS Galois self-dual codes using the above results. Some Galois self-dual codes and (almost) MDS Galois self-dual codes obtained in this paper turn out to be new.  相似文献   

13.
The result here answers the following questions in the affirmative: Can the Galois action on all abelian (Galois) fields $K/\mathbb{Q}$ be realized explicitly via an action on characters of some finite group? Are all subfields of a cyclotomic field of the form $\mathbb{Q}(\chi)$, for some irreducible character $\chi$ of a finite group G? In particular, we explicitly determine the Galois action on all irreducible characters of the generalized symmetric groups. We also determine the smallest extension of $\mathbb{Q}$ required to realize (using matrices) a given irreducible representation of a generalized symmetric group. Received: 18 February 2002  相似文献   

14.
This paper is principally concerned with the action of the absolute Galois group on a family of dessins d'enfants i.e. isomorphism classes of coverings of the projective line unramified outside three points. More precisely, we prove a generalisation of a conjecture proposed by Yu. Kotchetkov in 1997. The main tool used in this work is a correspondence between dessins d'enfants and ribbon graphs arising from the theory of Strebel differentials.  相似文献   

15.
This article provides necessary and sufficient conditions for each group of order 32 to be realizable as a Galois group over an arbitrary field. These conditions, given in terms of the number of square classes of the field and the triviality of specific elements in related Brauer groups, are used to derive a variety of automatic realizability results.  相似文献   

16.
Let K be a number field with ring of integers OK. Suppose a finite group G acts numerically tamely on a regular scheme X over OK. One can then define a de Rham invariant class in the class group Cl(OK[G]), which is a refined Euler characteristic of the de Rham complex of X. Our results concern the classification of numerically tame actions and the de Rham invariant classes. We first describe how all Galois étale G-covers of a K-variety may be built up from finite Galois extensions of K and from geometric covers. When X is a curve of positive genus, we show that a given étale action of G on X extends to a numerically tame action on a regular model if and only if this is possible on the minimal model. Finally, we characterize the classes in Cl(OK[G]) which are realizable as the de Rham invariants for minimal models of elliptic curves when G has prime order.  相似文献   

17.
Philippe Nuss 《代数通讯》2013,41(7):3223-3251
We study various types of noncommutative Galois extensions and present some examples. We state a criterion which decides whether a given automorphism of a Galois extension belongs to the corresponding Galois group or not. We then compute Borovoi’s nonabelian cohomology sets (in degree 0, 1, 2) of the Galois group with coefficients in a crossed module associated to the Galois extension.  相似文献   

18.
We discuss rather systematically the principle, implicit in earlier works, that for a “random” element in an arithmetic subgroup of a (split, say) reductive algebraic group over a number field, the splitting field of the characteristic polynomial, computed using any faitfhful representation, has Galois group isomorphic to the Weyl group of the underlying algebraic group. Besides tools such as the large sieve, which we had already used, we introduce some probabilistic ideas (large deviation estimates for finite Markov chains) and the general case involves a more precise understanding of the way Frobenius conjugacy classes are computed for such splitting fields (which is related to a map between regular elements of a finite group of Lie type and conjugacy classes in the Weyl group which had been considered earlier by Carter and Fulman for other purposes; we show in particular that the values of this map are equidistributed).  相似文献   

19.
We study Chebyshev?s bias in a finite, possibly nonabelian, Galois extension of global function fields. We show that, when the extension is geometric and satisfies a certain property, called, Linear Independence (LI), the less square elements a conjugacy class of the Galois group has, the more primes there are whose Frobenius conjugacy classes are equal to the conjugacy class. Our results are in line with the previous work of Rubinstein and Sarnak in the number field case and that of the first-named author in the case of polynomial rings over finite fields. We also prove, under LI, the necessary and sufficient conditions for a certain limiting distribution to be symmetric, following the method of Rubinstein and Sarnak. Examples are provided where LI is proved to hold true and is violated. Also, we study the case when the Galois extension is a scalar field extension and describe the complete result of the prime number race in that case.  相似文献   

20.
By considering the Galois action and the group action,we give the relationof two isomorphism character rings on the arbitrary field K with Char K=0.Our resultsgeneralize Saksonov's theorem.  相似文献   

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