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John Thompson | |
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John Thompson in 2007 | |

Born | Ottawa, Kansas, U.S. | October 13, 1932

Nationality | American |

Alma mater | Yale University (B.A. 1955) University of Chicago (Ph.D. 1959) |

Awards | Cole Prize (1965) Fields Medal (1970) Fellow of the Royal Society (1979) Senior Berwick Prize (1982) Sylvester Medal (1985) Wolf Prize (1992) Médaille Poincaré (1992) ^{ [1] }^{ [2] }National Medal of Science (2000) Abel Prize (2008) De Morgan Medal (2013) |

Scientific career | |

Fields | Group theory |

Institutions | Harvard University (1961–62) University of Chicago (1962–68) University of Cambridge (1968–93) University of Florida (1993–present) |

Thesis | A Proof that a Finite Group with a Fixed-Point-Free Automorphism of Prime Order is Nilpotent (1959) |

Doctoral advisor | Saunders Mac Lane |

Doctoral students | R. L. Griess Richard Lyons Charles Sims Nick Patterson |

**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.

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.^{ [3] }

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 *.^{ [4] }

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.

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.^{ [5] } He is a Fellow of the Royal Society (United Kingdom), and a recipient of its Sylvester Medal in 1985.^{ [6] } He is a member of the Norwegian Academy of Science and Letters.^{ [7] }

In mathematics, the **classification of the finite simple groups** is a theorem stating that every finite simple group belongs to one of four broad classes described below. These groups can be seen as the basic building blocks of all finite groups, in a way reminiscent of the way the prime numbers are the basic building blocks of the natural numbers. The Jordan–Hölder theorem is a more precise way of stating this fact about finite groups. However, a significant difference from integer factorization is that such "building blocks" do not necessarily determine a unique group, since there might be many non-isomorphic groups with the same composition series or, put in another way, the extension problem does not have a unique solution.

In mathematics, a **simple group** is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, namely a nontrivial normal subgroup and the corresponding quotient group. This process can be repeated, and for finite groups one eventually arrives at uniquely determined simple groups, by the Jordan–Hölder theorem.

In mathematics, **Galois theory** provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is in some sense simpler and better understood. It has been used to solve classic problems including showing that two problems of antiquity cannot be solved as they were stated ; showing that there is no quintic formula; and showing which polygons are constructible.

In mathematics, more specifically in the field of group theory, a **solvable group** or **soluble group** is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup.

**Jean-Pierre Serre** is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954 and the inaugural Abel Prize in 2003.

**Jacques Tits** is a Belgium-born French mathematician who works on group theory and incidence geometry. He introduced Tits buildings, the Tits alternative, the Tits group, and the Tits metric.

**John Torrence Tate Jr.** was an American mathematician, distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry. He was awarded the Abel Prize in 2010.

In abstract algebra, a **finite group** is a group, of which the underlying set contains a finite number of elements.

**Isadore Manuel Singer** is an American mathematician. He is an Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology and a Professor Emeritus of Mathematics at the University of California, Berkeley.

**Richard Dagobert Brauer** was a leading German and American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory. He was the founder of modular representation theory.

**Gregori Aleksandrovich Margulis** is a Russian-American mathematician known for his work on lattices in Lie groups, and the introduction of methods from ergodic theory into diophantine approximation. He was awarded a Fields Medal in 1978 and a Wolf Prize in Mathematics in 2005, becoming the seventh mathematician to receive both prizes. In 1991, he joined the faculty of Yale University, where he is currently the Erastus L. De Forest Professor of Mathematics.

In mathematics, the **Feit–Thompson theorem**, or **odd order theorem**, states that every finite group of odd order is solvable. It was proved by Walter Feit and John Griggs Thompson.

**Walter Feit** was an American mathematician who worked in finite group theory and representation theory. His contributions provided elementary infrastructure used in algebra, geometry, topology, number theory, and logic. His work helped the development and utilization of sectors like cryptography, chemistry, and physics.

The **history of group theory**, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical roots of group theory: the theory of algebraic equations, number theory and geometry. Joseph Louis Lagrange, Niels Henrik Abel and Évariste Galois were early researchers in the field of group theory.

**Gopal Prasad** is an Indian-American mathematician. His research interests span the fields of Lie groups, their discrete subgroups, algebraic groups, arithmetic groups, geometry of locally symmetric spaces, and representation theory of reductive p-adic groups.

In mathematical finite group theory, Thompson's original **uniqueness theorem** states that in a minimal simple finite group of odd order there is a unique maximal subgroup containing a given elementary abelian subgroup of rank 3. Bender (1973) gave a shorter proof of the uniqueness theorem.

In mathematical finite group theory, the **Dade isometry** is an isometry from class functions on a subgroup *H* with support on a subset *K* of *H* to class functions on a group *G*. It was introduced by Dade (1964) as a generalization and simplification of an isometry used by Feit & Thompson (1963) in their proof of the odd order theorem, and was used by Peterfalvi (2000) in his revision of the character theory of the odd order theorem.

In mathematical finite group theory, the **Thompson transitivity theorem** gives conditions under which the centralizer of an abelian subgroup *A* acts transitively on certain subgroups normalized by *A*. It originated in the proof of the odd order theorem by Feit and Thompson (1963), where it was used to prove the Thompson uniqueness theorem.

In mathematical representation theory, **coherence** is a property of sets of characters that allows one to extend an isometry from the degree-zero subspace of a space of characters to the whole space. The general notion of coherence was developed by Feit, as a generalization of the proof by Frobenius of the existence of a Frobenius kernel of a Frobenius group and of the work of Brauer and Suzuki on exceptional characters. Feit & Thompson developed coherence further in the proof of the Feit–Thompson theorem that all groups of odd order are solvable.

- ↑ Thompson, John Griggs — serge.mehl.free.fr
- ↑ Liste des 122 fondations Archived 2014-10-06 at the Wayback Machine . The
*médaille Poincaré*awarded by the French Academy of Sciences was eliminated in 1997 in favor of the*Grande Médaille*. - ↑ "Thompson and Tits share the Abel Prize for 2008". Norwegian Academy of Science and Letters. 2008-05-17. Archived from the original on 2008-05-20. 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".

- ↑ http://www.cecm.sfu.ca/organics/papers/lam/paper/html/NYTimes.html New York Times article, April 26, 1959.
- ↑ "John Griggs Thompson". University of St. Andrews. Retrieved 24 October 2016.
- ↑ "Royal Society Sylvester Medalists" . Retrieved 2 March 2014.
- ↑ "Gruppe 1: Matematiske fag" (in Norwegian). Norwegian Academy of Science and Letters. Archived from the original on 10 November 2013. Retrieved 7 October 2010.

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