CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES

<p>In this thesis, we have presented our discovery of true finite homomorphic images of various permutation and monomial progenitors, such as 2^*⁷: D₁₄, 2^*7: (7 : 2), 2^*6: S₃x 2, 2^*8: S₄, 2*⁷²: (3²:(2S₄)), and 11^*2 :_mD₁₀. We have given delightful symmetric presentations and very nice permutation representations of these images which include, the Mathieu groups M₁₁, M₁₂, the 4-fold cover of the Mathieu group M₂₂, 2 x L₂(8), and L₂(13). Moreover, we have given constructions, by using the technique of double coset enumeration, for some of the images, including M₁₁ and M₁₂. We have given proofs, either by hand or computer-based, of the isomorphism type of each image. In addition, we use Iwasawa's Lemma to prove that L₂(13) over A₅, L₂(8) over D₁₄, L₂(13) over D₁₄, L₂(27) over 2D₁₄, and M₁₁ over 2S₄ are simple groups. All of the work presented in this thesis is original to the best of our knowledge.</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

• Ramirez, Jessica Luna

Contributors dc:contributor

• Hasan, Zahid

• Group theory
• Mathieu groups
• linear groups
• construction
• Algebra

Repository record dc:identifier

https://scholarworks.lib.csusb.edu/etd/254

OAI identifier oai:identifier

oai:scholarworks.lib.csusb.edu:etd-1288