John G. Thompson
John Griggs Thompson ( born October 13, 1932 in Ottawa, Kansas, USA) is an American mathematician who is best known for work in group theory.
He received his B. A. from Yale University in 1955 and his doctorate in 1959 at the University of Chicago in the algebraists Saunders MacLane ("A proof did a finite group with a fixed-point - free automorphism of prime order is nilpotent " triggers a presumption of Ferdinand Georg Frobenius ). He then taught at Harvard from 1961 to 1962, at the University of Chicago and from 1968 in Cambridge, England (from 1970 he was there Rouse Ball Professor ) and at the University of Florida. At both universities he is emeritus today.
From Thompson originate substantial contributions to the classification of finite simple groups ( simple groups are groups without non-trivial normal subgroup and can thus as a kind of " primes " the group theory are considered ). His monumental evidence with Walter Feit that non- abelian finite simple groups have just order ( odd order paper), published in 1963 in the Pacific Journal of Mathematics ( Solvability of groups of odd order, Vol.13, S.775 -1023 ) and brought him the Fields Medal. The evidence showed that the classification of finite simple groups was " vulnerable ". In the following years he did a part of the program and classified the minimal finite simple groups (one without other groups as factor groups). Specifically, he classified the groups with solvable local subgroups. As a corollary is that a finite group is solvable if and only if every subgroup generated by two elements is solvable.
The Thompsongruppe Th, one of the sporadic finite simple groups, is named after him.
He also worked on the reverse of the Galois theory. He found a necessary criterion that finite groups are Galois groups ( the Monster group meets this criterion and is therefore symmetry group of an algebraic equation and can be fully characterized by specifying this equation ).
In 1966 he gave a plenary lecture at the International Congress of Mathematicians in Moscow ( Characterizations of Finite Simple Groups).
Among his doctoral students include David Goldschmidt, Robert Griess, Richard Lyons, Charles Sims.