John Griggs Thompson (born October 13, 1932, in Ottawa, Kansas, USA) is a mathematician noted for his work in the field of finite groups. He was awarded the Fields Medal in 1970 and the 2008 Abel Prize.

Biography

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. After spending some time on the Mathematics faculty at the University of Chicago, he moved in 1970 to the Rouse Ball Professorship in Mathematics at the University of Cambridge, England, and later moved to the Mathematics Department of the University of Florida as a Graduate Research Professor. He is currently a Professor Emeritus of Pure Mathematics at the University of Cambridge, and professor of mathematics at the University of Florida. He received the Abel Prize 2008 together with Jacques Tits.[1]

Work

Thompson's doctoral thesis already 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[2] (though, unfortunately, 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 paper 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.

Further recognition

In 1971, Thompson was elected to the United States National Academy of Sciences. In 1982, he was awarded the Senior Berwick Prize of the London Mathematical Society, and in 1988, he received the honorary degree of Doctor of Science from the University of Oxford. Thompson received the Wolf Prize in 1992, and is the only person other than Jean-Pierre Serre to have won all three of the Fields Medal, the Wolf Prize, and the Abel Prize. Thompson was awarded the United States National Medal of Science in 2000. He is a Fellow of the Royal Society (United Kingdom), and a recipient of its Sylvester Medal.

See also

* Feit–Thompson theorem
* Thompson subgroup
* McKay–Thompson series

References

1. ^ "Thompson and Tits share the Abel Prize for 2008". The Niels Henrik Abel Memorial Fund. 2008-05-17. Archived from the original on 2008-05-20. http://www.webcitation.org/5XxtY4s3z. Retrieved 2008-05-20. "The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2008 to John Griggs Thompson, University of Florida and Jacques Tits, Collège de France. This was announced by the Academy’s President, Ole Didrik Lærum, at a press conference in Oslo today. Thompson and Tits receives the Abel Prize “for their profound achievements in algebra and in particular for shaping modern group theory”."
2. ^ http://www.cecm.sfu.ca/organics/papers/lam/paper/html/NYTimes.html New York Times article, April 26, 1959.

External links

* O'Connor, John J.; Robertson, Edmund F., "John G. Thompson", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Thompson_John.html .
* John G. Thompson at the Mathematics Genealogy Project
* List of mathematical articles by John G. Thompson
* Biography from the Abel Prize center