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Asymptotic Results for Primitive Permutation Groups and Irreducible Linear Groups

✍ Scribed by A. Lucchini; F. Menegazzo; M. Morigi

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 135 KB
Volume: 223
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8081

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✦ Synopsis

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 2 d 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,

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