Multiply transitive group action ($t\text{-transitive}$)

A group action is $t$-transitive if it acts transitively on ordered $t$-tuples of distinct points. In degree $n\ge t$ this implies $n(n-1)\cdots (n-t+1)\mid |G|$. It is sharply t-transitive when each such ordered tuple has trivial stabilizer subgroup.

Transitivity on ordered triples of distinct points. It implies a two-transitive group action, but is stronger: in projective dimension at least two, collinear and noncollinear triples distinguish two orbits, even though the projective action is two-transitive.