Asymptotic Results for Primitive Permutation Groups and Irreducible Linear Groups
Asymptotic Results for Primitive Permutation Groups and Irreducible Linear Groups
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原置换群和不可约线性群的渐近结果
DOI：
10.1006/jabr.1999.8081
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发表时间：
2000
影响因子：
0.9
通讯作者：
M. Morigi
中科院分区：
文献类型：
--
作者：
A. Lucchini;F. Menegazzo;M. Morigi
渐近群理论的一个发展良好的分支研究线性群和置换群的类作为其度的函数的性质。我们参考了卡梅隆[4]和派伯[17，18]的调查以及派伯和沙莱夫[19]最近的论文，以详细阐述这一主题。在本文中，我们集中我们的注意力在发电机的数量。我们的结果，像最近的结果在这方面，取决于有限的简单群（这将被称为CFSG）的分类。关于线性群，1991年Kovács和罗宾逊[11]证明了每个维数为d的有限完全可约线性群可以由3个2d元生成，之后，1993年Bryant等人[3]证明了以下结果：对于每个素子域上的度有限的域F，
A well-developed branch of asymptotic group theory studies the properties of classes of linear and permutation groups as functions of their degree. We refer to the surveys of Cameron [4] and Pyber [17, 18] and the recent paper by Pyber and Shalev [19] for a detailed exposition of this subject. In this paper we concentrate our attention on the number of generators. Our results, like most recent results in this area, depend on the classification of finite simple groups (which will be referred to hereafter as CFSG). Concerning linear groups, in 1991, Kovács and Robinson [11] proved that every finite completely reducible linear group of dimension d can be generated by 3 2d elements, and afterwards, in 1993, Bryant, et al. [3] proved the following result: to each field F whose degree over its prime subfield is finite,