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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 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.
Original language | English |
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Pages (from-to) | 2415-2467 |
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
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DP0770915 - APF - Praeger - ARF/QE11 - Giudici - Finite Permutation Groups and Flag-Transitive Incidence Structures
Praeger, C., Giudici, M., Li, C. & Penttila, T.
1/01/07 → 31/12/11
Project: Research