有限线性群Jordan定理的模类比
Modular analogues of Jordan's theorem for finite linear groups
摘要：
1878年，Jordan证明了GL（n，C）的有限子群包含一个阿贝尔正规子群，其指数仅由n的函数有界。在此之前，作者给出了精确的界限。这里，我们考虑正特征l的代数闭域上有限线性群的类似物。为了消除幂幺子群和特征为l的Lie型群，必须取一个较大的正规子群，并且我们证明了它的界一般类似于特征0 -为（n+1）！，或（n+2）！当L整除（n+2）时，由对称群的最小次数的忠实表示给出.对于所有的度n和每个特征l，给出了最优界的完整答案。
英文摘要：
In 1878, Jordan showed that a finite subgroup of GL(n,C) contains an abelian normal subgroup whose index is bounded by a function of n alone. Previously, the author has given precise bounds. Here, we consider analogues for finite linear groups over algebraically closed fields of positive characteristic l. A larger normal subgroup must be taken, to eliminate unipotent subgroups and groups of Lie type and characteristic l, and we show that generically the bound is similar to that in characteristic 0 - being (n+1)!, or (n+2)! when l divides (n+2) - given by the faithful representations of minimal degree of the symmetric groups. A complete answer for the optimal bounds is given for all degrees n and every characteristic l.
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