Definition:Transitive Subgroup

Definition
Let $S_n$ denote the symmetric group on $n$ letters for $n \in \N$.

Let $H$ be a subgroup of $S_n$.

Let $H$ be such that:
 * for every pair of elements $i, j \in \N_n$ there exists $\pi \in H$ such that $\map \pi i = j$.

Then $H$ is called a transitive subgroup of $S_n$.