Mathematical Sciences: A Parabolic Classification of the Quasi-thin Finite Simple Groups

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This project is concerned with classifying the quasi-thin finite simple groups by means of the amalgam method. The principal investigator will analyze the weak (B,N)-pairs of rank three corresponding to a reducible rank 2 parabolic. In addition, he will determine the "small" amalgams. The classification of finite simple groups has been a major concern for the past several decades with implications for many areas of algebra. This research is concerned with streamlining and revising portions of this classification, resulting in a clearer understanding of the area. Simultaneously, it will provide new insights into the geometry of these groups.