Algebra Commons^™

Homomorphic Images And Related Topics, Kevin J. Baccari

Electronic Theses, Projects, and Dissertations

We will explore progenitors extensively throughout this project. The progenitor, developed by Robert T Curtis, is a special type of infinite group formed by a semi-direct product of a free group m^*n and a transitive permutation group of degree n. Since progenitors are infinite, we add necessary relations to produce finite homomorphic images. Curtis found that any non-abelian simple group is a homomorphic image of a progenitor of the form 2^*n: N. In particular, we will investigate progenitors that generate two of the Mathieu sporadic groups, M₁₁ and M₁₁, as well as …

Symmetric Presentations And Related Topics, Mashael U. Alharbi

Electronic Theses, Projects, and Dissertations

In this thesis, we have presented our discovery of symmetric presentations of a number of non-abelian simple groups, including the Mathieu group M₁₂. We have given several progenitors, permutation and monomial, including 2*⁴:(2²:3), 2*⁵:D₁₀, 2*⁸:((4X2).D₄), 3*⁷:_m L₂(7), 2*⁶:(Z₃ wr Z₂), and 2*²⁴: (2^. A₅) and their homomorphic images which include 4.(M₁₂:2), the group of automorphisms of M₁₂ and several classical groups. We have given the isomorphism type of …

A Fundamental Unit Of O_K, Susana L. Munoz

Electronic Theses, Projects, and Dissertations

In the classical case we make use of Pells equation to compute units in the ring O_F. Consider the parallel to the classical case and the quadratic field extension that creates the ring O_K. We use the generalized Pell's equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute its units.

Homormophic Images And Their Isomorphism Types, Diana Herrera

Electronic Theses, Projects, and Dissertations

In this thesis we have presented original homomorphic images of permutations and monomial progenitors. In some cases we have used the double coset enumeration tech- nique to construct the images and for all of the homomorphic images that we have discovered, the isomorphism type of each group is given. The homomorphic images discovered include Linear groups, Alternating groups, and two sporadic simple groups J₁ and J₂X2 where J₁ is the smallest Janko group and J₂ is the second Janko sporadic group.

Monoid Rings And Strongly Two-Generated Ideals, Brittney M. Salt

Electronic Theses, Projects, and Dissertations

This paper determines whether monoid rings with the two-generator property have the strong two-generator property. Dedekind domains have both the two-generator and strong two-generator properties. How common is this? Two cases are considered here: the zero-dimensional case and the one-dimensional case for monoid rings. Each case is looked at to determine if monoid rings that are not PIRs but are two-generated have the strong two-generator property. Full results are given in the zero-dimensional case, however only partial results have been found for the one-dimensional case.

The Irreducible Representations Of D2n, Melissa Soto

Electronic Theses, Projects, and Dissertations

Irreducible representations of a finite group over a field are important because all representations of a group are direct sums of irreducible representations. Maschke tells us that if φ is a representation of the finite group G of order n on the m-dimensional space V over the field K of complex numbers and if U is an invariant subspace of φ, then U has a complementary reducing subspace W .

The objective of this thesis is to find all irreducible representations of the dihedral group D2n. The reason we will work with the dihedral group is because it is one …