Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 20 of 20
Full-Text Articles in Physical Sciences and Mathematics
A Study Of Finite Symmetrical Groups, May Majid
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
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
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
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.
A Study On The Modular Structures Of Z₂S₃ And Z₅S₃, Bethany Michelle Tasaka
A Study On The Modular Structures Of Z₂S₃ And Z₅S₃, Bethany Michelle Tasaka
Theses Digitization Project
This project is a study of the properties of the modules Z₂S₃ and Z₅S₃, which are examined both as modules over themselves and as modules over their respective integer fields. Each module is examined separately since they each hold distinct properties. The overall goal is to determine the simplicity and semisimplicity of each module.
Symmetric Presentation Of Finite Groups, Thuy Nguyen
Symmetric Presentation Of Finite Groups, Thuy Nguyen
Theses Digitization Project
The main goal of this project is to construct finite homomorphic images of monomial infinite semi-direct products which are called progenitors. In this thesis, we provide an alternative convenient and efficient method. This method can be applied to many groups, including all finite non-abelian simple groups.
Symmetric Generation Of M₂₂, Bronson Cade Lim
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
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
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
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.
On A Symmetric Presentation Of The Double Cover Of M₂₂: 2, Gabriela Laura Maerean
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).
The Universal Coefficient Theorem For Cohomology, Michael Anthony Rosas
The Universal Coefficient Theorem For Cohomology, Michael Anthony Rosas
Theses Digitization Project
This project is an expository survey of the Universal Coefficient Theorem for Cohomology. Algebraic preliminaries, homology, and cohomology are discussed prior to the proof of the theorem.
Symmetric Representation Of Elements Of Finite Groups, Timothy Edward George
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 Generation Of Finite Homomorphic Images?, Lee Farber
Symmetric Generation Of Finite Homomorphic Images?, Lee Farber
Theses Digitization Project
The purpose of this thesis was to present the technique of double coset enumeration and apply it to construct finite homomorphic images of infinite semidirect products. Several important homomorphic images include the classical groups, the Projective Special Linear group and the Derived Chevalley group were constructed.
Symmetric Representation Of Elements Of Sporadic Groups, Elena Yavorska Harris
Symmetric Representation Of Elements Of Sporadic Groups, Elena Yavorska Harris
Theses Digitization Project
Uses the techniques of symmetric presentations to manipulate elements of large sporadic groups and to represent elements of these groups in much shorter forms than their corresponding permutation or matrix representation. Undertakes to develop a nested algorithm and a computer program to manipulate elements of large sporadic groups.
Symmetrically Generated Groups, Benny Nguyen
Symmetrically Generated Groups, Benny Nguyen
Theses Digitization Project
This thesis constructs several groups entirely by hand via their symmetric presentations. In particular, the technique of double coset enumeration is used to manually construct J₃ : 2, the automorphism group of the Janko group J₃, and represent every element of the group as a permutation of PSL₂ (16) : 4, on 120 letters, followed by a word of length at most 3.
Symmetric Generation Of Finite Groups, MaríA De La Luz Torres Bisquertt
Symmetric Generation Of Finite Groups, MaríA De La Luz Torres Bisquertt
Theses Digitization Project
Advantages of the double coset enumeration technique include its use to represent group elements in a convenient shorter form than their usual permutation representations and to find nice permutation representations for groups. In this thesis we construct, by hand, several groups, including U₃(3) : 2, L₂(13), PGL₂(11), and PGL₂(7), represent their elements in the short form (symmetric representation) and produce their permutation representations.
Symmetric Representations Of Elements Of Finite Groups, Abeir Mikhail Kasouha
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.
Various Steiner Systems, Valentin Jean Racataian
Various Steiner Systems, Valentin Jean Racataian
Theses Digitization Project
This project deals with the automorphism group G of a Steiner system S (3, 4, 10). S₁₀, the symmetrical group of degree 10, acts transitively on T, the set of all Steiner systems with parameters 3, 4, 10. The purpose of this project is to study the action of S₁₀ on cosets of G. This will be achieved by means of a graph of S₁₀ on T x T. The orbits of S₁₀ on T x T are in one-one correspondence with the orbits of G, the stabilizer of an S [e] T on T.
Homomorphic Images Of Semi-Direct Products, Lamies Joureus Nazzal
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.