G_2型Chevalley群的第一Cartan不变量

On the First Cartan Invariant for Chevalley Group of Type G^2

设K是特征数p>0的代数闭域,G是K上G_2型单连通半单代数群,G(n)是p^n个元素的有限域Fp^n上与G同型的Chevalley群.本文主要结果:当p≥13时,p个元素的有限域FP上G_2型Chevalley群的第一Cartan不变量C_(11)=224.

Let G he a simply connected semisimple algebraic group over an alge-braically closed field K of character istic p>0. Let G(n) be a finite group consisting of fixed points of the Frobenius morphism Fo of G. The main result of this paper is that the first Cartan invariant for chev-alley group of type G, over a finite field Fp, p≥13, is 224.