John G. Thompson

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John Griggs Thompson (born 13 Oct 1932) is a mathematician noted for his work in the field of finite groups. He received his B.A. from Yale University in 1955 and his doctorate from the University of Chicago in 1959 under the supervision of Saunders Mac Lane. In 1970 he moved to Cambridge, England, and later moved to the University of Florida.

Thompson was a key figure in the progress toward the classification of finite simple groups. In 1963, he and Walter Feit proved that all nonabelian finite simple groups are of even order (the Odd Order Paper, filling a whole issue of the Pacific Journal of Mathematics). In the next few years he classified all the minimal finite simple groups: those that contain no other simple groups as subquotients. This work was later extended by many mathematicians to the classification of finite simple groups. Thompson received the Fields Medal in 1970.

He has also made major contributions to the inverse Galois problem. He found a criterion for a finite group to be a Galois group, that in particular implies that the monster simple group is a Galois group.

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