Highly transitive group action

Symbol-free definition
A group action is termed highly transitive if it is $$k$$-transitive (in the sense of a multiply transitive group action) for every positive integer $$k$$.

Weaker properties

 * Stronger than::Highly set-transitive group action
 * Stronger than::Triply transitive group action
 * Stronger than::Doubly transitive group action
 * Stronger than::Primitive group action
 * Stronger than::Transitive group action