Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Generating finite completely reducible linear groups


Authors: L. G. Kovács and Geoffrey R. Robinson
Journal: Proc. Amer. Math. Soc. 112 (1991), 357-364
MSC: Primary 20H20
DOI: https://doi.org/10.1090/S0002-9939-1991-1047004-0
MathSciNet review: 1047004
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is proved here that each finite completely reducible linear group of dimension $ d$ (over an arbitrary field) can be generated by $ \left\lfloor {\frac{3}{2}d} \right\rfloor $ 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 $ {\mathbb{O}_p}\left( G \right)$ 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/{\mathbb{O}_p}\left( G \right)$ can still be generated by $ \left\lfloor {\frac{3}{2}d} \right\rfloor $ elements.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20H20

Retrieve articles in all journals with MSC: 20H20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1047004-0
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society