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Date of Award

12-2017

Document Type

Restricted Thesis: Campus only access

Degree Name

Master of Arts in Mathematics

Department

Mathematics

First Reader/Committee Chair

Hasan, Zahid

Abstract

We have investigated several monomial and permutation progenitors, including

2*8 : [8 : 2], 2*18 : [(22 x 3) : (3x2)], 2*16 : [22 : 4], and 2*16 : 24,

5*2 :m [422], 5*2 :m [(4x2) : 2], 103∗2 :m [17 : 2] and 103∗4 :m [17 : 4]. We have discovered original, to the best of our knowledge, symmetric presentations of a number of finite groups, including PSL(2, 7), M12 , A6 : 2, A7 , PSL(2, 25), 25 : S4,

24 : S3, PSL(2, 271), 12 x PSL(2, 13), and U(3, 7) : 2. We will present our construction of several of these images, including the Mathieu sporadic simple group M12 over the maximal subgroup PSL(2, 11), PSL(2, 17) over D9, PSL(2, 16) : 2 over [24 : 5] and PGL(2, 7) over S3. We will also give our method of finding isomorphism classes of images.

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