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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 57 for “"Class Group"”.
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The Structure of the Class Group of Imaginary Quadratic Fields
… Δ. We use the isomorphism between the ideal class groups of the field and the equivalence classes of binary quadratic forms to find the structure of the class group. We determine the structure by combining two of Shanks' algorithms [7, 8]. We utilize this method to find fields with cyclic …
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Homology of Configuration Spaces of Surfaces as Mapping Class Group Representations
… viewed as representations of the mapping class group of the surface, distinguishing between various flavours: ordered and unordered configurations, of closed surfaces and surfaces with boundary, and with different homology coefficients. In Chapter 2, we prove a version of the scanning …
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Comparison of and Improvements to Degree Zero Divisor Class Group Arithmetic in Algebraic Function Fields
This thesis develops improved algorithms for Jacobian arithmetic in global function fields and compares the improvements to previous works. We present two independent improvements to Jacobian arithmetic based on the unique representation described in [13]. The first improvement requires the …
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Improved Arithmetic in the Ideal Class Group of Imaginary Quadratic Number Fields with an Application to Integer Factoring
… to arithmetic and exponentiation in the ideal class group of imaginary quadratic number fields for the Intel x64 architecture. This is useful in tabulating the class number and class group structure, but also as an application to a novel integer factoring algorithm called “SuperSPAR”. SuperSPAR …
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A computation of the action of the mapping class group on isotopy classes of curves and arcs in surfaces
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1982.
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Visualizing Geometric Structures on Topological Surfaces
… internal measures unchanged. The language of groups gives us a way to distinguish geometric structures. Understanding the mapping class group is an important and hard problem. This paper contributes to visualizing how the mapping class group acts on geometric structures. We explore the …
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The quantum Johnson homomorphism and symplectomorphism of 3-folds
introduce a subset K2,A of the symplectic mapping class group, and an invariant ... that associates a characteristic class in Hochschild cohomology to every symplectomorphism ... K2,A. These are analogues to the familiar Johnson kernel X9 and second Johnson homomorphism - 2 from low-dimensional …
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Least dilatation of pure surface braids
… thesis finds its roots in the Nielsen-Thurston classification of the mapping class group, a result that is fundamental to the field of low dimensional topology. In particular, Thurston's work gives us a powerful normal form for mapping classes: up to taking powers and restricting to subsurfaces, …
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On the Galois module structure of the units and ray classes of a real abelian number field
… the Galois module structure of the ideal ray class group and the group of units of a real abelian number field. Specifically, we derive explicit annihilators of the ideal ray class groups in the vein of the classical Stickelberger theorems. This is made possible by generalizing a theorem of …
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The effects of grouping fourth grade students into cooperative learning groups by learning patterns
… grade students working in cooperative learning groups. Students worked in three cooperative learning groups in order to determine whether grouping students heterogeneously into cooperative learning groups based on individual students' learning pattern would have a positive correlation with group …
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The Structure of the 2-Sylow Subgroups of the Ideal Class Groups of Imaginary Bicyclic Biquadratic Fields
In this dissertation class groups of imaginary bicyclic biquadratic fields are considered. In chapter 1 we develop a method for determining the structure of the 2-class group of K. In chapters 3, 4, and 5 this method is applied to determine all imaginary bicyclic biquadratic extensions of Q with …
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Subgroups of the Torelli group
Let Mod(Sg) be the mapping class group of an orientable surface of genus g, Sg. The action of Mod(Sg) on the homology of Sg induces the well-known symplectic representation: <BR> <BR> <center>Mod(Sg) ---> Sp(2g, Z).</center> <BR> The kernel of this representation is called the Torelli group, I(Sg). …
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Explicit Composition Identities for Higher Composition Laws in the Quadratic Case
… useful way to compute the structure of ideal class groups in quadratic number fields. In addition to that, Gauss composition is also important in the problem of representations of integers by binary quadratic forms. In 2001, Bhargava discovered a new approach to Gauss composition which uses …
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Combinatorial models for surface and free group symmetries
… representation of a surface mapping class group by describing its action on simple closed curves. Similar complexes of spheres, free factors, and free splittings allow combinatorial representation of the automorphisms of a free group. We consider a Birman exact sequence for …
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An Equal-Distribution Result for Galois Module Structure
… ring of integers o, and let G be a fixed finite group. If K$\sb\pi$ is a tame Galois G-extension, the integral closure ${\cal O}\sb\pi$ of o in K$\sb\pi$ is a locally free rank one oG-module, so realizes a class cl(${\cal O}\sb\pi$) in the locally free class group Cl(oG). We let R(oG) denote the …
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Quintic Abelian Fields
… in terms of their conductor and a certain Galois group. From these, a generating polynomial and its roots and an integral basis are computed. A method for finding the fundamental units, regulators and class numbers is then developed. Tables listing the coefficients of a generating polynomial, the …
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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 …
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Reading Achievement of General Education Children in Blended Classes
… special needs students into the regular classroom has any effect on the reading achievement of the general education student. To accomplish this, the examiner found two comparable groups from the current sixth grade class. Group A was the integrated students and Group B was the …
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Two mod-p Johnson filtrations
We consider two mod-p central series of the free group given by Stallings and Zassenhaus. Applying these series to definitions of Dennis Johnson's filtration of the mapping class group we obtain two mod-p Johnson filtrations. Further, we adapt the definition of the Johnson homomorphisms to obtain …
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Effects of the working class label: increased affect and social class identification
… model of the self, we show that relatively lower-class individuals who value their social class identity (as activated by the “working class” label) experience elevated group identification and well-being. First, we found that social class identification significantly predicted self-esteem while …
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