Arithmetic results on orbits of linear groups
Publisher
AMER MATHEMATICAL SOCCitation
Arithmetic results on orbits of linear groups 2015, 368 (4):2415 Transactions of the American Mathematical SocietyRights
Copyright © 2015 American Mathematical Society. First published in Trans. Amer. Math. Soc. 368 (April 2016), published by the American Mathematical Society.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.Abstract
Let p be a prime and G a subgroup of GL(d)(p). We define G to be p-exceptional if it has order divisible by p, but all its orbits on vectors have size coprime to p. We obtain a classification of p-exceptional linear groups. This has consequences for a well-known conjecture in representation theory, and also for a longstanding question concerning 1/2-transitive linear groups (i.e. those having all orbits on nonzero vectors of equal length), classifying those of order divisible by p.Note
Article electronically published on August 19, 2015.ISSN
0002-99471088-6850