 Multiply transitive group action

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.

In group theory, a branch of abstract algebra, the concept of **group action** describes how a group operates on a set. A group action can be defined mathematically, and it captures the essence of symmetry in algebraic structures.