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A Character Condition for Quadruple Transitivity

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  • S. Aldhafeeri
  • R. T. Curtis

Abstract

Let ð º be a permutation group of degree ð ‘› viewed as a subgroup of the symmetric group 𠑆 ≅ 𠑆 ð ‘› . We show that if the irreducible character of 𠑆 corresponding to the partition of ð ‘› into subsets of sizes ð ‘› − 2 and 2, that is, to say the character often denoted by 𠜒 ( ð ‘› − 2 , 2 ) , remains irreducible when restricted to ð º , then ð ‘› = 4, 5 or 9 and ð º â‰… 𠑆 3 , A 5 , or PΣL 2 (8), respectively, or ð º is 4-transitive.

Suggested Citation

  • S. Aldhafeeri & R. T. Curtis, 2011. "A Character Condition for Quadruple Transitivity," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-13, August.
    • Handle: RePEc:hin:jijmms:757134
    DOI: 10.1155/2011/757134
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