Work
Thompson's doctoral thesis introduced powerful and innovative techniques, and included the solution of a problem in finite group theory which had stood for around sixty years, the nilpotency of Frobenius kernels. At the time, this achievement was noted in The New York Times (though his university affiliation was stated incorrectly there).
Thompson became 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). This work was recognised by the award of the 1965 Cole Prize in Algebra of the American Mathematical Society. His monumental N-group papers classified all finite simple groups for which the normalizer of every non-identity solvable subgroup is solvable. This included, as a by-product, the classification of all minimal finite simple groups (those for which every proper subgroup is solvable). This work had great influence on later developments in the classification of finite simple groups, and was quoted in the citation by Richard Brauer for the award of Thompson's Fields Medal in 1970 (Proceedings of the International Congress of Mathematicians, Nice, France, 1970)..
The Thompson group Th is one of the 26 sporadic finite simple groups. Thompson 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.
Read more about this topic: John G. Thompson
Famous quotes containing the word work:
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—Bruce Grocott (b. 1940)
“As a man has no right to kill one of his children if it is diseased or insane, so a man who has made the gradual and conscious expression of his personality in literature the aim of his life, has no right to suppress himself any carefully considered work which seemed good enough when it was written. Suppression, if it is deserved, will come rapidly enough from the same causes that suppress the unworthy members of a man’s family.”
—J.M. (John Millington)
“Those who work their minds rule; those who work with their backs are ruled.”
—Chinese proverb.
Mencius.