Homomorphic Images And Related Topics

<p>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 some classical groups. We will prove their existences a variety of different ways, including the process of double coset enumeration, Iwasawa's Lemma, and linear fractional mappings. We will also investigate the various techniques of finding finite images and their corresponding isomorphism types.</p>

Name thesis:degree_name

Master of Arts in Mathematics

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2015

Author dc:creator

• Baccari, Kevin J

Contributors dc:contributor

• Hasan, Zahid

• progenitors
• MAGMA
• Iwasawa's
• Double Coset Enumeration
• Isomorphism Type
• Algebra

Repository record dc:identifier

https://scholarworks.lib.csusb.edu/etd/224

OAI identifier oai:identifier

oai:scholarworks.lib.csusb.edu:etd-1218