Generating finite completely reducible linear groups
Generating finite completely reducible linear groups
复制标题
生成有限完全可约线性群
DOI：
10.1090/s0002-9939-1991-1047004-0
复制
发表时间：
1991
期刊：
影响因子：
--
通讯作者：
J. Wong
中科院分区：
文献类型：
--
作者：
Author L. G. Kovács;Geoffrey R. Robinson;L. Kovács;Geoffrey R. Robinson;J. Wong
证明了每个有限完全可约的d维线性群(在任意域上)都可以由L元生成。如果一个维为d的有限线性群G不是完全可约的，则它的特征是素数p，且G的模为最大正规p-子群的因子群P(G)可视为作用于G的自然模的合成因子的直和的完全可约线性群：因此，G/IOP(G)仍可由L3D]元生成。
It is proved here that each finite completely reducible linear group of dimension d (over an arbitrary field) can be generated by L 3 d] elements. If a finite linear group G of dimension d is not completely reducible, then its characteristic is a prime, p say, and the factor group of G modulo the largest normal p-subgroup O.p(G) may be viewed as a completely reducible linear group acting on the direct sum of the composition factors of the natural module for G: consequently, G/IOp(G) can still be generated by L3d] elements.