Generalizing a classical theorem of Jordan to arbitrary characteristic,
we prove that every finite subgroup of GLn
over a field of any characteristic
p possesses a subgroup of bounded index which is composed of finite simple
groups of Lie type in characteristic p, a commutative group of order prime
to p, and a p-group. While this statement can be deduced from the
classification of finite simple groups, our proof is self-contained and uses
methods only from algebraic geometry and the theory of linear algebraic
groups. We believe that our results can serve as a viable substitute for
classification in a range of applications in various areas of mathematics.
Dieser Eintrag ist Teil der Universitätsbibliographie.
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