Homormophic Images and their Isomorphism Types

In this thesis we have presented original homomorphic images of permutations and monomial progenitors. In some cases we have used the double coset enumeration tech- nique to construct the images and for all of the homomorphic images that we have discovered, the isomorphism type of each group is given. The homomorphic images discovered include Linear groups, Alternating groups, and two sporadic simple groups J1 and J2X2 where J1 is the smallest Janko group and J2 is the second Janko sporadic group