Abstract:
A specific type of mathematical construct, called a finite simple group, is the subject of this paper. The information presented attempts to be comprehensive in the fact that it covers a broad range of topics connected to finite simple groups. A historical overview is given along with a survey of both past and present research. The direction and purpose of this research is explained in addition to mentioning those papers of key significance.
Simplicity, the special property possessed by all finite simple groups, is given a concrete foundation through definitions and frequent comparisons with the prime numbers. Each of the four types of finite simple groups are discussed within the limitations of the length of the paper and the technical knowledge of the author.
Since all finite simple groups are now known, they can be used to construct any finite group imaginable. This fundamental nature of finite simple groups is justified in this thesis with major theorems and examples. Miscellaneous facts, uniquely associated with finite simple groups, serves as a conclusion.
