### Abstract

Original language | English |
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Pages (from-to) | 2415-2467 |

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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### Cite this

*Transactions of the American Mathematical Society*,

*368*(4), 2415-2467. https://doi.org/10.1090/tran/6373

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*Transactions of the American Mathematical Society*, vol. 368, no. 4, pp. 2415-2467. https://doi.org/10.1090/tran/6373

**Arithmetic results on orbits of linear groups.** / Giudici, Michael; Liebeck, M.W.; Praeger, Cheryl; Saxl, J.; Tiep, P.H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Arithmetic results on orbits of linear groups

AU - Giudici, Michael

AU - Liebeck, M.W.

AU - Praeger, Cheryl

AU - Saxl, J.

AU - Tiep, P.H.

PY - 2016/4

Y1 - 2016/4

N2 - © 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.

AB - © 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.

U2 - 10.1090/tran/6373

DO - 10.1090/tran/6373

M3 - Article

VL - 368

SP - 2415

EP - 2467

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 4

ER -