Transitive Subgroup/Examples/n-Cycle
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Example of Transitive Subgroup
Let $S_n$ denote the symmetric group on $n$ letters for $n \in \N$.
Consider the subgroup $H$ of $S_n$ generated by the cyclic permutation $\tuple {1, 2, \ldots, n}$.
Then $H$ is a transitive subgroup .
Sources
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Symmetric Groups: $\S 86$