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1.
We propound a descent principle by which previously constructed equations over GF(q
n)(X) may be deformed to have incarnations over GF(q)(X) without changing their Galois groups. Currently this is achieved by starting with a vectorial (= additive)q-polynomial ofq-degreem with Galois group GL(m, q) and then, under suitable conditions, enlarging its Galois group to GL(m, q
n) by forming its generalized iterate relative to an auxiliary irreducible polynomial of degreen. Elsewhere this was proved under certain conditions by using the classification of finite simple groups, and under some other
conditions by using Kantor’s classification of linear groups containing a Singer cycle. Now under different conditions we
prove it by using Cameron-Kantor’s classification of two-transitive linear groups. 相似文献
2.
A general technique is developed to enlarge the Galois group of an equation from a subgroup of a finite classical isometry
group towards the corresponding similitude group.
Abhyankar’s work was partly supported by NSF grant DMS 97-32592 and NSA grant MDA 904-97-1-0010, and Loomis’s work was partly
supported by a Sloan Doctoral Dissertation Fellowship. 相似文献
3.
A. Vourdas 《Journal of Fourier Analysis and Applications》2008,14(1):102-123
Complex functions χ(m) where m belongs to a Galois field GF(p
ℓ
), are considered. Fourier transforms, displacements in the GF(p
ℓ
)×GF(p
ℓ
) phase space and symplectic transforms of these functions are studied. It is shown that the formalism inherits many features
from the theory of Galois fields. For example, Frobenius transformations and Galois groups are introduced in the present context.
The relationship between harmonic analysis on GF(p
ℓ
) and harmonic analysis on its subfields, is studied.
相似文献
4.
Anthony Manning 《Proceedings Mathematical Sciences》1995,105(3):269-271
A givenn ×n matrix of rational numbers acts onC
π and onQ
π. We assume that its characteristic polynomial is irreducible and compare a basis of eigenvectors forC
π with the standard basis forQ
π. Subject to a hypothesis on the Galois group we prove that vectors from these two bases are as independent of each other
as possible. 相似文献
5.
J. Gómez-Torrecillas 《Applied Categorical Structures》2006,14(5-6):579-598
We investigate which aspects of recent developments on Galois corings and comodules admit a formulation in terms of comonads.
The general theory is applied to the study of Galois comodules over corings over firm rings.
Supported by the research project “Algebraic Methods in Non Commutative Geometry,” with financial support of the grant MTM2004-01406
from the DGICYT and FEDER. 相似文献
6.
A criterion for the existence of a birational embedding with two Galois points for quotient curves is presented. We apply our criterion to several curves, for example, some cyclic subcovers of the Giulietti–Korchmáros curve or of the curves constructed by Skabelund. New examples of plane curves with two Galois points are described, as plane models of such quotient curves. 相似文献
7.
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
8.
Joost Vercruysse 《数学学报(英文版)》2008,24(10):1655-1674
We show the close connection between apparently different Galois theories for comodules introduced recently in [J. Gomez-Torrecillas and J. Vercruysse, Comatrix corings and Galois Comodules over firm rings, Algebr. Represent. Theory, 10 (2007), 271 306] and [Wisbauer, On Galois comodules, Comm. Algebra 34 (2006), 2683-2711]. Furthermore we study equivalences between categories of comodules over a coring and modules over a firm ring. We show that these equivalences are related to Galois theory for comodules. 相似文献
9.
We classify the precrossed module central extensions using the second cohomology group of precrossed modules. We relate these central extensions to the relative central group extensions of Loday, and to other notions of centrality defined in general contexts. Finally we establish a Universal Coefficient Theorem for the (co)homology of precrossed modules, which we use to describe the precrossed module central extensions in terms of the generalized Galois theory developed by Janelidze. 相似文献
10.
We introduce group corings, and study functors between categories of comodules over group corings, and the relationship to
graded modules over graded rings. Galois group corings are defined, and a Structure Theorem for the G-comodules over a Galois group coring is given. We study (graded) Morita contexts associated to a group coring. Our theory
is applied to group corings associated to a comodule algebra over a Hopf group coalgebra.
This research was supported by the research project G.0622.06 “Deformation quantization methods for algebras and categories
with applications to quantum mechanics” from Fonds Wetenschappelijk Onderzoek-Vlaanderen. The third author was partially supported
by the SRF (20060286006) and the FNS (10571026). 相似文献
11.
We give an infinite family of intersective polynomials with Galois group A 4, the alternating group on four letters. 相似文献
12.
Fix a prime number . We prove a conjecture stated by Ihara, which he attributes to Deligne, about the action of the absolute Galois group on the pro- completion of the fundamental group of the thrice punctured projective line. Similar techniques are also used to prove part of a conjecture of Goncharov, also about the action of the absolute Galois group on the fundamental group of the thrice punctured projective line. The main technical tool is the weighted completion of a profinite group with respect to a reductive representation (and other appropriate data). 相似文献
13.
S. Caenepeel E. De Groot J. Vercruysse 《Transactions of the American Mathematical Society》2007,359(1):185-226
El Kaoutit and Gómez-Torrecillas introduced comatrix corings, generalizing Sweedler's canonical coring, and proved a new version of the Faithfully Flat Descent Theorem. They also introduced Galois corings as corings isomorphic to a comatrix coring. In this paper, we further investigate this theory. We prove a new version of the Joyal-Tierney Descent Theorem, and generalize the Galois Coring Structure Theorem. We associate a Morita context to a coring with a fixed comodule, and relate it to Galois-type properties of the coring. An affineness criterion is proved in the situation where the coring is coseparable. Further properties of the Morita context are studied in the situation where the coring is (co)Frobenius.
14.
We study the degree of elimination of imaginaries needed for the three main applications: to have canonical bases for types over models, to define strong types as types over algebraically closed sets and to have a Galois correspondence between definably closed sets B such that A ? B ? acl(A) and closed subgroups of the Galois group Aut(acl(A)/A). We also characterize when the topology of the Galois group is the quotient topology. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
《代数通讯》2013,41(9):3437-3457
Abstract The notions of group coalgebra Galois extension and group entwining structure are defined. It is proved that any group coalgebra Galois extension induces a unique group-entwining map ψ = {ψα, β}α, β∈π compatible with the right group coaction, generalizing the recent work of Brzeziński and Hajac [Brzeziński, T., Hajac, P. M. (1999). Coalgebra extensions and algebra coextensions of Galois type. Comm. Algebra 27:1347–1368]. 相似文献
16.
By introducing the conception “relativistic differential Galois group” for the second order polynomial systems, we establish the relation between the conformal relativistic differential Galois group and the subgroup of Möbius transformations, and prove that the system is integrable in the sense of Liouville if its conformal relativistic differential Galois group is solvable with a derived length at most 2. Some omissions on the structures of solvable subgroups of Möbius transformations at the first author’s article published in this journal in 1996 are refreshed in this paper. 相似文献
17.
Yoshiyuki Tomiyama 《Journal of Number Theory》2010,130(10):2214-2222
It is proved that every two-dimensional residual Galois representation of the absolute Galois group of an arbitrary number field lifts to a characteristic zero p-adic representation, if local lifting problems at places above p are unobstructed. 相似文献
18.
H. Markšaitis 《Lithuanian Mathematical Journal》2000,40(1):39-47
LetK
p (p, q) be the maximalp-extension of the field ℚ of rational numbers with ramification pointsp andq. LetG
p (p, q) be the Galois group of the extensionK
p(p.q)/ℚ. It is known thatG
p(p, q) can be presented by two generators which satisfy a single relation. The form of this relation is known only modulo
the second member of the descending central series ofG
p(p, q). In this paper, we find an arithmetical-type condition on which the form of the relation modulo the third member of
the descending central series ofG
p(p, q) depends. We also consider two examples withp=3,q=19 andp=3,q=37.
Translated from Lietuvos Matematikos Rinkinys, Vol. 40, No. 1, pp. 48–60, January–March, 2000.
Translated by H. Markšaitis 相似文献
19.
Symmetric function theory provides a basis for computing Galois groups which is largely independent of the coefficient ring. An exact algorithm has been implemented over in Maple for degree up to 8. A table of polynomials realizing each transitive permutation group of degree 8 as a Galois group over the rationals is included.
20.
Ke-ying GUAN & Jin-zhi LEI School of Science Beijing Jiaotong University Beijing China Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing China 《中国科学A辑(英文版)》2007,(5)
By introducing the conception "relativistic differential Galois group" for the second order polynomial systems, we establish the relation between the conformal relativistic differential Galois group and the subgroup of Mobius transformations, and prove that the system is integrable in the sense of Liouville if its conformal relativistic differential Galois group is solvable with a derived length at most 2. Some omissions on the structures of solvable subgroups of Mobius transformations at the first author's article published in this journal in 1996 are refreshed in this paper. 相似文献