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LINEAR GROUPS WITH ORDERS HAVING CERTAIN LARGE PRIME DIVISORS

Published online by Cambridge University Press:  01 January 1999

ROBERT GURALNICK ,
TIM PENTTILA ,
CHERYL E. PRAEGER  and
JAN SAXL
ROBERT GURALNICK
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1113, U.S.A. E-mail:[email protected]
TIM PENTTILA
Affiliation:
Department of Mathematics, University of Western Australia, Perth, WA 6907, Australia. E-mail:[email protected]; [email protected]
CHERYL E. PRAEGER
Affiliation:
Department of Mathematics, University of Western Australia, Perth, WA 6907, Australia. E-mail:[email protected]; [email protected]
JAN SAXL
Affiliation:
Department of Pure Mathematics and Mathematical Statistics ,16 Mill Lane Cambridge, CB2 1SB. E-mail:[email protected]
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Abstract

In this paper we obtain a classification of those subgroups of the finite general linear group $\mbox{GL}_d (q)$ with orders divisible by a primitive prime divisor of $q^e - 1$ for some $e > \frac{1}{2}d$. In the course of the analysis, we obtain new results on modular representations of finite almost simple groups. In particular, in the last section, we obtain substantial extensions of the results of Landazuri and Seitz on small cross-characteristic representations of some of the finite classical groups.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 78 , Issue 1 , January 1999 , pp. 167 - 214
Copyright
© 1999 The London Mathematical Society

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