International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 757134, 13 pages
Research Article

A Character Condition for Quadruple Transitivity

School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

Received 9 May 2011; Accepted 22 June 2011

Academic Editor: Frank Werner

Copyright © 2011 S. Aldhafeeri and R. T. Curtis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let 𝐺 be a permutation group of degree 𝑛 viewed as a subgroup of the symmetric group 𝑆 𝑆 𝑛 . We show that if the irreducible character of 𝑆 corresponding to the partition of 𝑛 into subsets of sizes 𝑛 2 and 2, that is, to say the character often denoted by 𝜒 ( 𝑛 2 , 2 ) , remains irreducible when restricted to 𝐺 , then 𝑛 = 4, 5 or 9 and 𝐺 𝑆 3 , A5, or PΣL2(8), respectively, or 𝐺 is 4-transitive.