Journal of the Australian Mathematical Society (Series A)

Table of Contents - 1978 - Volume 25, Issue 02  

Research Article

On the normal structure of a one-point stabilizer in a doubly transitive permutation group

M. D. Atkinsona1 and Cheryl E. Praegera2

a1 Department of Computing Mathematics University College Cardiff, Wales

a2 Department of Mathematics University of Western Australia Nedlands, Australia 6009

Let G be a doubly transitive permutation group on a finite set Ω, and let Kα be a normal subgroup of the stabilizer Gα of a point α in Ω. If the action of Gα on the set of orbits of Kα in Ω − {α} is 2-primitive with kernel Kα it is shown that either G is a normal extension of PSL(3, q) or Kα xs2229 Gγ is a strongly closed subgroup of Gαγ in Gα, where γ xs2208 Ω − {α}. If in addition the action of Gα on the set of orbits of Kα is assumed to be 3-transitive, extra information is obtained using permutation theoretic and centralizer ring methods. In the case where Kα has three orbits in Ω − {α} strong restrictions are obtained on either the structure of G or the degrees of certain irreducible characters of G. Subject classification (Amer. Math. Soc. (MOS) 1970: 20 B 20, 20 B 25.

(Received March 08 1977)

Subject classification (Amer. Math. Soc. (MOS) 1970)

  • 20 B 20;
  • 20 B 25