On subgroups ofGLn(Fp)
On subgroups ofGLn(Fp)
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关于 GLn(Fp) 的子群
DOI：
10.1007/bf01388909
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发表时间：
1987
影响因子：
3.1
通讯作者：
M. Nori
中科院分区：
文献类型：
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作者：
M. Nori
设G是GL（Fp）的子群.令X={x~ G1 × V = 1}。表示定义在Fv上的GL的（连通）代数子群，由对所有xeX的单参数子群t~-* xt= exp（t log x）生成。由X生成的G的（正规）子群记为G+。我们的主要结果（见定理B，w 3）说，如果素数p大于某个只依赖于n的常数，则G § = G（Fv）+。若G是半单单连通的，则d（F~）= d（F）+，从而G+=（~（Fp））.换句话说，G §被实现为连通代数群G的有理点的群。
Let G be a subgroup of GL,(Fp). Let X={x~ GlxV= l}. Denote by (~ the (connected) algebraic subgroup of GL,, defined over Fv, generated by the oneparameter subgroups t~-* xt= exp (t log x) for all xeX. The (normal) subgroup of G generated by X is denoted by G+. Our main result (see Theorem B, w 3) says that if the prime p is greater than some constant that depends only on n, then G § = G (Fv)+. If G is semi-simple and simply connected, then d (F~)= d (F)+ and therefore G+=(~(Fp) in this case. In other words, G § is realized as the group of rational points of the connected algebraic group G.