## Thursday, March 27, 2008

### 2008 Abel Prize: Thompson and Tits

The 2008 Abel Prize for mathematics
is shared by John Griggs Thompson (Florida) and Jacques Tits (France). It is a great victory for group theory and symmetries.

Both mathematicians have played a key role in the multi-decadal project of the classification of all finite groups.

John Griggs Thompson (*1932) has also solved the problem of the nilpotency of Frobenius kernels. He proved the even parity of the order of simple non-Abelian groups, classified various groups satisfying constraints on various normalizers. The Thompson group is one of the sporadic groups. It may be obtained from a centralizer of a type 3C element of the monster group or as a subgroup of the Chevalley group E8(F3), a reason why the Thompson group has a 248-dimensional representation.

You might think that giving an Abel prize for non-Abelian groups is paradoxical but believe me, giving USD 1.2 million for Abelian groups would be even more crazy. ;-)

Jacques Tits (*1930), a Belgian mathematician, was an honorary member of the infamous ultra-rigorous Nicolas Bourbaki group. However, not everything is an excrement if it looks dark. ;-) Tits is the guy who has coined the terms such as "Coxeter number", "Coxeter group", and "Coxeter graph". You may have heard of the Tits group, the "simplest" or "most classical" among the sporadic groups (occasionally included among groups of Lie type): it is the derived subgroup of the twisted Chevalley group 2F4(2).