Definition:Transitive Subgroup
Jump to navigation
Jump to search
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:
Then $H$ is called a transitive subgroup of $S_n$.
Examples
$n$-Cycle in $S_n$
Consider the subgroup $H$ of $S_n$ generated by the cyclic permutation $\tuple {1, 2, \ldots, n}$.
Then $H$ is a transitive subgroup .
Also see
- Results about transitive subgroups can be found here.
Sources
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Symmetric Groups: $\S 86$