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Wilcox, Elizabeth

Mathematics

2006

MS

Many real world and mathematical objects exhibit symmetries, which can be successively combined (or "multiplied") to create new symmetries. This law of "multiplication" led to the formulation of abstract structures known as groups, and the study of group theory has become a main branch in modern mathematics. A fundamental result in group theory is that groups containing only a finite number of elementscan be "uniquely factored," similar to the unique factorization of integers, with so-called simple groups being the analog of prime numbers. One of the major mathematical results in the last century was the determination of the complete list of all finite simple groups: the Classification of Finite Simple Groups. This Theorem, in its original form, requires some 15,000 journal pages spanning about 500 articles by more than 100 mathematicians (written mostly between 1940 and 1980). A cornerstone of this Classification is a famous paper by Michio Suzuki on so-called CA-groups. Our work is an attempt to shed new light on the Pivotal CA-group proof, at least in special cases, by using different techniques than Suzuki, such as methods from permutation group theory and graph theory.