Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 12 of 12 for “"Galois groups"”.
-
Calculation of Galois groups
<p>In the 19th Century Galois developed a method for determining whether an equation is solvable. It relied on the close relationship between fields and their automorphism group. This paper is a survey of the techniques of Galois theory. After presenting the main results of elementary Galois theory …
-
Galois Groups With Restricted Ramification
U of I Only
-
Difference equations with semisimple Galois groups in positive characteristic
… Picard-Vessiot ring, one can assign a difference Galois group to the Picard-Vessiot ring, which turns out to be a linear algebraic group (in the scheme theoretic sense). Let F = F_q(s,t) with sigma defined to be the automorphism that fixes F_q(t) pointwise and maps s to s^q. The main result of …
-
On the Complexity of Computing Galois Groups of Differential Equations
<p>The differential Galois group is an analogue for a linear differential equation of the classical Galois group for a polynomial equation. An important application of the differential Galois group is that a linear differential equation can be solved by integrals, exponentials and algebraic …
-
On A Conjecture of Pal Turan and Investigations Into Galois Groups of Generalized Laguerre Polynomials
… <p>In the second half we investigate the Galois groups associated with the generalized Laguerre polynomials. We are able to classify Laguerre polynomials with the alternating group as the Galois group. We further compute the Galois groups in certain particular cases.</p>
-
On the Inverse Problem in Differential Galois Theory
Differential Galois theory generalizes the usual Galois theory for polynomials to differential equations. There is the notion of a splitting field (Picard-Vessiot extension) of a differential equation, and the differential Galois group is the group of automorphisms of this extension which fix the …
-
On Greenberg's question: an algebraic and computational approach
… up into four cases, depending on properties of Galois groups. This analysis is then used to give a positive answer to Greenberg’s question in some nontrivial examples.
-
Units and class groups of imaginary octic fields
In this dissertation class groups and unit groups of number fields with elementary Galois groups of order 4 and 8 are considered. In chapter 3 we consider bicyclic biquadratic extensions K/k and give a method for determining the structure of the 2-class group of K. In chapters 4 and 5 this method …
-
Arboreal representations, sectional monodromy groups, and abelian varieties over finite fields
… first part studies arboreal representations of Galois groups - an arithmetic dynamics analogue of Tate modules - and proves some large image results, in particular confirming a conjecture of Odoni. Given a field K, a separable polynomial [mathematical expression], and an element [mathematical …
-
Iterative Connections and Abhyankar's Conjecture
… with the problem which linear algebraic groups occur as iterative differential Galois groups of IPV-extensions with restricted singular locus. In this thesis, I prove the differential Abhyankar conjecture for connected groups and give necessary and sufficient conditions for connected …
-
Geometry of the Hitchin Morphism and Spectral Correspondences
… covers of the complex projective line through Galois-theoretic arguments. The proof relies upon a classification of Galois groups into primitive and imprimitive types. In this context, we revisit a classical theorem of Ritt. We move to examining the image of Hitchin morphism on algebraic …
-
Local Conjugations of Groups and Applications to Number Fields
This dissertation studies pairs of subgroups H, H' of a finite group G together with a bijective map Φ H −> H' that is a local conjugation, meaning that each element h in H is conjugate in G to its image Φ(h). The map Φ is not required to take products to products. The motivation for studying such …