# John G. Thompson

Wolf Prize Laureate in Mathematics 1992

**John G. Thompson**

#### Affiliation at the time of the award:

**University of Cambridge****, U.K**

#### Award citation:

**“for his profound contributions to all aspects of finite group theory and connections with other branches of mathematics”.**

#### Prize share:

**John G. Thompson**

**Lennart Carleson**

Professor John G. Thompson’s work has changed the face of finite group theory. Already in his thesis he solved a long-standing conjecture reaching back to work of Frobenius at the turn of the century: if a finite group has a fixed-point-free automorphism of finite order, then the group is nilpotent. The solution was obtained by the introduction of novel and highly original ideas. He next turned his attention to the classification of the finite simple groups. The first astonishing achievement was his joint Mark with Walter Feit in which they prove that a finite non-abelian simple group must have even order. Thompson went on to classify the finite simple groups in which every soluble subgroup has a soluble normalizer. This work is a key element in the collective effort that led to the classification of finite simple groups.

In the late 1970’s he took up McKay’s remarkable observation, that there is a connection between the Fischer-Griess group and the modular j-function to formulate a series of conjectures relating modular functions and finite sporadic simple groups. These have now been verified and have led to deep and important questions which will occupy mathematicians for some time to come.

Also during this period he significantly contributed to coding theory and the theory of finite projective planes. The recent solution of the classical problem of the non-existence of a plane of order 10 owes much to his efforts.

During the past few years he has investigated the problem of constructing Galois groups over number fields, especially Q. The starting point here is Hilbert’s irreducibility Theorem and Thompson´s work may well be the most important advance since Hilbert’s time.

The penetrating power of Thompson’s genius is astonishing; his contributions to group theory and related subjects are of enduring significance.