Simple Groups and Related Topics

Since every nonabelian simple group is a homomorphic image of an involutory progenitor 2^(*n):N where N ≤ S_n is transitive, our motivation for the thesis has been to seek finite homomorphic images of such progenitors and construct them using our technique of double coset enumeration. We have constructed U_3 (3):2 over 5^2:S_3, 2x(A_5 x A_5) over D_5 x D_5, S_6 over S_5, 2^5:S_5 over S_5, and 3^3: 2^3 over 3^2:2 . We have discovered original symmetric presentations numerous group as homomorphic images various progenitors. We have also found new monomial representations of groups and given monomial progenitors. We have given isomorphism class of every image that we have discovered