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Linear Groups with Orders Having Certain Large Prime Divisors
Author(s) -
Guralnick Robert,
Penttila Tim,
Praeger Cheryl E.,
Saxl Jan
Publication year - 1999
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611599001616
Subject(s) - mathematics , prime (order theory) , divisor (algebraic geometry) , classification of finite simple groups , section (typography) , mathematics subject classification , simple (philosophy) , prime factor , simple group , sylow theorems , modular form , pure mathematics , group (periodic table) , combinatorics , finite group , algebra over a field , group of lie type , group theory , philosophy , chemistry , organic chemistry , epistemology , advertising , business
In this paper we obtain a classification of those subgroups of the finite general linear group GL d ( q ) with orders divisible by a primitive prime divisor of q e − 1 for some e > 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. 1991 Mathematics Subject Classification : primary 20G40; secondary 20C20, 20C33, 20C34, 20E99.