Date of Award


Document Type


Degree Name

Master of Arts in Mathematics



First Reader/Committee Chair

Hasan, Zahid


The aim of this thesis is to generate original symmetric presentations for finite non-abelian simple groups. We will discuss many permutation progenitors, including but not limited to 2*14 : D28, 29 : 3(32), 39 : 3(32), 221 : (7X3) : 2 as well as monomial progenitors, including 75 :m A5, 35 :m S5. We have included their homomorphic images which include the Mathieu group M12, 2J2, 2XS(4, 5), as well as, many PGLs, PSLs and alternating groups. We will give proofs of the isomorphism types of each progenitor, either by hand using double coset enumeration or computer based using MAGMA. We have also constructed Cayley graphs of the following groups, 25 : S5 over 25 : S5, PSL(2, 8) over 27 : D14, M12 over a maximal subgroup, 2XS5. We have developed a lemma using relations to factor permutation progenitors of the form mn : N to give an isomorphism of mn : N . Motivated by Robert T. Curtis’ research, we will present a program using MAGMA that, when given a target finite non-abelian simple group, the program will generate possible control groups to write progenitors that will give the given finite non-abelian simple group. Iwasawa’s lemma is also discussed and used to prove PSL(2, 8) and M12 to be simple groups.

Included in

Algebra Commons