Simple Groups and Related Topics

<p>In this thesis, we will give our discovery of original symmetric presentations of several important groups. We have investigated permutation and monomial progenitors 2^*8: (2³: 2²), 2*9: (3²: 2⁴), 2^*10: (2⁴: (2 × 5)), 5^*4:_m (2³: 2²), 7^*8:_m (3²: 2⁴), and 3^*5:_m (2⁴: (2 × 5)). The finite images of the above progenitors include the Mathieu sporadic group M₁₂, the linear groups L₂(8) and L₂(13), and the extensions S₆ × 2, 2⁸ : .L₂(8) , and 2⁷ : .A₅. We will show our construction of the four groups S₃ , L₂(8), L₂(13), and S₆ × 2 over S₃, 2², S₃ : 2, and S₅, by using the technique of double coset enumeration. We will also provide isomorphism types all of the groups that have appeared as finite homomorphic images. We will show that the group L₂(8) does not satisfy the conditions of Iwasawas Lemma and that the group L₂(13) is simple by Iwasawas Lemma. We give constructions of M₂₂ × 2 and M₂₂ as homomorphic images of the progenitor S₆.</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

• Marouf, Manal Abdulkarim, Ms.

Contributors dc:contributor

• Zahid Hasan

• Symple Groups
• linear group
• extensions Homomorphic Image
• Isomorphicm Type
• Progenitor
• Group
• Permutation
• Monomial
• Character
• Classes
• Magma
• Double Coset Enumeration
• Mathieu sporadic group
• Physical Sciences and Mathematics

Repository record dc:identifier

https://scholarworks.lib.csusb.edu/etd/239

OAI identifier oai:identifier

oai:scholarworks.lib.csusb.edu:etd-1272