Permutation and Monomial Progenitors

Author

Crystal DiazFollow

Date of Award

6-2020

Document Type

Thesis

Degree Name

Master of Arts in Mathematics

Department

Mathematics

First Reader/Committee Chair

Hasan, Zahid

Abstract

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.

Recommended Citation

Diaz, Crystal, "Permutation and Monomial Progenitors" (2020). Electronic Theses, Projects, and Dissertations. 1086.
https://scholarworks.lib.csusb.edu/etd/1086