doubly transitive groups are primitive


Every doubly transitive group is primitive (


Let G acting on X be doubly transitive. To show the action is , we must show that all blocks are trivial blocks; to do this, it suffices to show that any block containing more than one element is all of X. So choose a block Y with two distinct elements y1,y2. Given an arbitrary xX, since G is doubly transitive, we can choose σG such that


But then σYY, since y1 is in both. Thus σY=Y, so xY as well. So Y=X and we are done. ∎

Title doubly transitive groups are primitive
Canonical name DoublyTransitiveGroupsArePrimitive
Date of creation 2013-03-22 17:21:50
Last modified on 2013-03-22 17:21:50
Owner rm50 (10146)
Last modified by rm50 (10146)
Numerical id 7
Author rm50 (10146)
Entry type Theorem
Classification msc 20B15