AffiliationUniv Arizona, Dept Math
MetadataShow full item record
PublisherAMER MATHEMATICAL SOC
CitationArithmetic results on orbits of linear groups 2015, 368 (4):2415 Transactions of the American Mathematical Society
RightsFirst published in Trans. Amer. Math. Soc. 368 (April 2016), published by the American Mathematical Society. Copyright 2015 American Mathematical Society.
Collection InformationThis 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 firstname.lastname@example.org.
AbstractLet 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.
NoteArticle electronically published on August 19, 2015.
VersionFinal accepted manuscript
SponsorsThe first four authors acknowledge the support of an ARC Discovery Grant; the first author acknowledges the support of an Australian Research Fellowship; the third author acknowledges the support of a Federation Fellowship; the fifth author acknowledges the support of the NSF (grants DMS-0901241 and DMS-1201374).