John Griggs Thompson

John Griggs Thompson (2007)

John Griggs Thompson (born October 13, 1932 in Ottawa , Kansas , USA ) is an American mathematician , who is particularly known for work in group theory .

Life

He received his BA from Yale University in 1955 and his doctorate in 1959 from the University of Chicago with the algebraic Saunders MacLane (" A proof that a finite group with a fixed-point-free automorphism of prime order is nilpotent " solves a conjecture by Ferdinand Georg Frobenius ). He then taught at Harvard from 1961 to 1962 , at the University of Chicago and from 1968 in Cambridge in England (from 1970 he was Rouse Ball Professor there ) and at the University of Florida . Today he has retired from both universities.

Thompson made important contributions to the classification of finite simple groups (simple groups are groups without non-trivial normal divisors and can thus be viewed as a kind of “atom” in group theory). His monumental proof with Walter Feit that non-Abelian finite simple groups have even order (odd order paper) appeared in 1963 in the Pacific Journal of Mathematics ( Solvability of groups of odd order , vol. 13, pp. 775-1023) and is known today as the Feit-Thompson Theorem . The proof showed that the classification of finite simple groups was "vulnerable". In the following years he carried out part of the program and classified the minimal finite simple groups (excluding simple groups other than factor groups ). More precisely, he classified the groups with resolvable local subgroups. As a corollary it is valid that a finite group is solvable if and only if every subgroup that is generated by two elements is solvable. For this follow-up work in particular, he received the Fields Medal .

The Thompson group Th, one of the sporadic finite simple groups , is named after him.

He also worked on reversing Galois theory. He found a necessary criterion for the fact that finite groups are over Galois groups (the monster group fulfills this criterion, is therefore a symmetry group of an algebraic equation and can be fully characterized by specifying this equation). ${\displaystyle \mathbb {Q} }$

In 1966 he gave a plenary lecture at the International Congress of Mathematicians in Moscow (Characterizations of Finite Simple Groups).

His doctoral students include David Goldschmidt , Robert Griess , Richard Lyons , Charles Sims .

Awards

• 1965 Colepreis (with Walter Feit)
• 1970 Fields Medal
• 1971 member of the National Academy of Sciences
• 1985 New Year's Eve Medal from the Royal Society
• 1992 Wolf Prize and Poincaré Medal from the French Academy of Sciences
• 1998 member of the American Academy of Arts and Sciences
• 2008 Abel Prize (with Jacques Tits ), for fundamental contributions to algebra
• 2013 De Morgan Medal

literature

• Richard Brauer , laudation for Fields Medal, ICM, Nice 1970

See also

• Feit-Thompson conjecture

Web links

• Publication list University of Florida
• John J. O'Connor, Edmund F. Robertson :  John Griggs Thompson. In: MacTutor History of Mathematics archive .
• Thompson at the Mathematics Genealogy Project
• Gorenstein, Lyons, Solomon "The classification of the finite simple groups", 1994, AMS Books online , Vol. 2 from 1996 is here: [1]
• Some of Thompson's essays in the Proceedings of the National Academy are online here (for example A solvability criterium for finite groups and some consequences 1962): [2]
• Some of Thompson's essays from the Mathematische Zeitschrift are online here: [3]

Individual evidence

1. ↑ Thompson, Nonsolvable finite groups all of whose subgroups are solvable, Bulletin AMS, Volume 74, 1968, pp. 383-437, the other parts appeared in Pacific J. of Math., Part 2, Volume 33, 1970, 451-536 , Part 3, Volume 39, 1971, pp. 483-534, Part 3, Volume 48, 1973, pp. 511-592, Part 4, Volume 50, 1974, pp. 215-297, Part 5, Volume 51, 1974 , Pp. 573-630. So-called N-Group treatises by Thompson
2. ↑ Richard Brauer, laudation on the Fields medal by Thompson, ICM Nice 1970, Volume 1, pp. 15-16