Arithmetic results on orbits of linear groups

Michael Giudici, Martin W. Liebeck, Cheryl E. Praeger, Jan Saxl, Pham Huu Tiep

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Abstract

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 languageEnglish (US)
Pages (from-to)2415-2467
Number of pages53
JournalTransactions of the American Mathematical Society
Volume368
Issue number4
DOIs
StatePublished - Apr 2016

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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