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Theses Digitization Project

Theses/Dissertations

Group theory

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A Study Of Finite Symmetrical Groups, May Majid Jan 2013

A Study Of Finite Symmetrical Groups, May Majid

Theses Digitization Project

This study investigated finite homomorphic images of several progenitors, including 2*⁵ : S₅, 2*⁶ : A₆, and 3*⁵ : C₅ The technique of manual of double coset enumeration is used to construct several groups by hand and computer-based proofs are given for the isomorphism types of the groups that are not constructed.


A Study Of Finite Symmetrical Groups, Patrick Kevin Martinez Jan 2013

A Study Of Finite Symmetrical Groups, Patrick Kevin Martinez

Theses Digitization Project

This study discovered several important groups that involve the classical and sporadic groups. These groups appeared as finite homomorphic images of the progenitors 3*8 : PGL₂(7), 2*¹⁴ : L₃ (2), 5*³ : S₃ and 7*2 : m S₃.


Enumeration And Symmetric Presentations Of Groups, With Music Theory Applications, Jesse Graham Train Jan 2013

Enumeration And Symmetric Presentations Of Groups, With Music Theory Applications, Jesse Graham Train

Theses Digitization Project

The purpose of this project is to construct groups as finite homomorphic images of infinite semi-direct products. In particular, we will construct certain classical groups and subgroups of sporadic groups, as well groups with applications to the field of music theory.


Monomial And Permutation Representation Of Groups, Rebeca Maria Blanquet Jan 2012

Monomial And Permutation Representation Of Groups, Rebeca Maria Blanquet

Theses Digitization Project

The purpose of this project is to introduce another method of working with groups, that is more efficient when the groups we wish to work with are of a significantly large finite order. When we wish to work with small finite groups, we use permutations and matrices. Although these two methods are the general methods of working with groups, they are not always efficient.


Symmetric Generation, Lisa Sanchez Jan 2012

Symmetric Generation, Lisa Sanchez

Theses Digitization Project

The purpose of this project is to conduct a systematic search for finite homomorphic images of infinite semi-direct products mn : N, where m = 2,3,5,7 and N <̲ Sn and construct by hand some of the important homomorphic images that emerge from the search.


Symmetric Generation Of M₂₂, Bronson Cade Lim Jan 2011

Symmetric Generation Of M₂₂, Bronson Cade Lim

Theses Digitization Project

This study will prove the Mathieu group M₂₂ contains two symmetric generating sets with control grougp L₃ (2). The first generating set consists of order 3 elements while the second consists of involutions.


Homomorphic Images Of Progenitors Of Order Three, Mark Gutierrez Jan 2010

Homomorphic Images Of Progenitors Of Order Three, Mark Gutierrez

Theses Digitization Project

The main purpose of this thesis is to construct finite groups as homomorphic images of infinite semi-direct products, 2*n : N, 3*n : N, and 3*n :m N, where 2*n and 3*n are free products of n copies of the cyclic group C₂ extended by N, a group of permutations on n letters.


Symmetric Generators Of Order 3, Stewart Contreras Jan 2010

Symmetric Generators Of Order 3, Stewart Contreras

Theses Digitization Project

The main purpose of this project is to construct finite homomorphic images of infinite semi-direct products.


Symmetric Generation, Dung Hoang Tri Jan 2010

Symmetric Generation, Dung Hoang Tri

Theses Digitization Project

In this thesis we construct finite homorphic images of infinite semi-direct products, 2*n : N, where 2*n is a free product of n copies the cyclic group of permutations on n letter.


An Investigation Of Kurosh's Theorem, Keith Anthony Earl Jan 2010

An Investigation Of Kurosh's Theorem, Keith Anthony Earl

Theses Digitization Project

The purpose of this project will be an exposition of the Kurosh Theorem and the necessary and suffcient condition that A must be algebraic and satisfy a P.I. to be locally finite.


On A Symmetric Presentation Of The Double Cover Of M₂₂: 2, Gabriela Laura Maerean Jan 2009

On A Symmetric Presentation Of The Double Cover Of M₂₂: 2, Gabriela Laura Maerean

Theses Digitization Project

The purpose of this project is to construct finite homomorphic images of infinite semi-direct products. We will construct two finite homomorphic images, L₂ (8) and PGL₂ (9) of the infinite semi-direct product 2*³ : S₃. The main part of this project is to construct the double cover 2 - M₂₂ : 2 and the automorphism group M₂₂ : 2 of the Matheiu sporadic group M₂₂ as a homomorphic image of the progenitor 2*⁷ : L₃ (2).


Symmetric Representation Of Elements Of Finite Groups, Timothy Edward George Jan 2006

Symmetric Representation Of Elements Of Finite Groups, Timothy Edward George

Theses Digitization Project

The purpose of the thesis is to give an alternative and more efficient method for working with finite groups by constructing finite groups as homomorphic images of progenitors. The method introduced can be applied to all finite groups that possess symmetric generating sets of involutions. Such groups include all finite non-abelian simple groups, which can then be constructed by the technique of manual double coset enumeration.


Symmetric Representations Of Elements Of Finite Groups, Abeir Mikhail Kasouha Jan 2004

Symmetric Representations Of Elements Of Finite Groups, Abeir Mikhail Kasouha

Theses Digitization Project

This thesis demonstrates an alternative, concise but informative, method for representing group elements, which will prove particularly useful for the sporadic groups. It explains the theory behind symmetric presentations, and describes the algorithm for working with elements represented in this manner.


Homomorphic Images Of Semi-Direct Products, Lamies Joureus Nazzal Jan 2004

Homomorphic Images Of Semi-Direct Products, Lamies Joureus Nazzal

Theses Digitization Project

The main purpose of this thesis is to describe methods of constructing computer-free proofs of existence of finite groups and give useful techniques to perform double coset enumeration of groups with symmetric presentations over their control groups.


Presentations Of Direct Products Of Metacyclic Groups, Jared Everett Derksen Jan 1997

Presentations Of Direct Products Of Metacyclic Groups, Jared Everett Derksen

Theses Digitization Project

No abstract provided.


An Efficient Presentation Of Pgl(2,P), Theresa Marie Hert Jan 1993

An Efficient Presentation Of Pgl(2,P), Theresa Marie Hert

Theses Digitization Project

No abstract provided.