John Griggs Thompson (born October 13, 1932)
is a mathematician at the University of Florida
noted for his work in the field of finite
groups.
He was awarded the Fields Medal in 1970, the
Wolf Prize in 1992 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.
== Work ==
Thompson's doctoral thesis introduced new
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.
Thompson became a 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 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 (simple
groups for which every proper subgroup is
solvable).
This work had some 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.
== Awards ==
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 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 in 1985.
He is a member of the Norwegian Academy of
Science and Letters.
== See also ==
Feit–Thompson theorem
McKay–Thompson series
Quadratic pair
Thompson factorization
Thompson order formula
Thompson subgroup
Thompson transitivity theorem
Thompson uniqueness theorem
== References ==
== External links ==
O'Connor, John J.; Robertson, Edmund F., "John
G. Thompson", MacTutor History of Mathematics
archive, University of St Andrews.
John G. Thompson at the Mathematics Genealogy
Project
List of mathematical articles by John G. Thompson
Biography from the Abel Prize center
