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On the Number of Generators and Composition Length of Finite Linear Groups

✍ Scribed by A Lucchini; F Menegazzo; M Morigi

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 151 KB
Volume: 243
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8882

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✦ Synopsis

In 1991 Dixon and Kovacs 8 showed that for each field K which has finite degree over its prime subfield there is a number d such that every K finite nilpotent irreducible linear group of degree n G 2 over K can be w x wx ' generated by d nr log n elements. Afterwards Bryant et al. 3 proved K ' d G F q d nr log n for some absolute constants and . 1 2 1 2

Ž . We recall that an irreducible subgroup G of GL V is called quasi-K primitive if every normal subgroup of G is homogeneous on V. The study of the particular case of quasi-primitive linear groups plays a crucial role 1 Research partially supported by M.U.R.S.T. of Italy.

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