Date of Award


Document Type


Degree Name

Master of Arts in Mathematics



First Reader/Committee Chair

Hasan, Zahid


We searched monomial and permutation progenitors for symmetric presentations of important images, nonabelian simple groups, their automorphism groups, or groups that have these as their factor groups. In this thesis, we described our search for the homomorphic images through the permutation progenitor 2*15:(D5 X 3) and construction of a monomial representation through the group 23:3.

We constructed PGL(2,7) over 23:3 on 6 letters and L2(11) over 22:3 on 8 letters. We also give our construction of S5 X 2 and L2(25) as homomorphic images of the monomial progenitor 3*3:mD4. In addition, we describe how to solve the extension problem for finite groups through the example of the group (4X22):.A4.