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Abstract
© 2015 American Mathematical Society. Let p be a prime and G a subgroup of GLd(p). We define G to be pexceptional if it has order divisible by p, but all its orbits on vectors have size coprime to p. We obtain a classification of pexceptional linear groups. This has consequences for a wellknown 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.
Original language  English 

Pages (fromto)  24152467 
Number of pages  53 
Journal  Transactions of the American Mathematical Society 
Volume  368 
Issue number  4 
Early online date  19 Aug 2015 
DOIs  
Publication status  Published  Apr 2016 
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Dive into the research topics of 'Arithmetic results on orbits of linear groups'. Together they form a unique fingerprint.Projects
 1 Finished

DP0770915  APF  Praeger  ARF/QE11  Giudici  Finite Permutation Groups and FlagTransitive Incidence Structures
Praeger, C., Giudici, M., Li, C. & Penttila, T.
1/01/07 → 31/12/11
Project: Research