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Can anybody tell me what is known about the classification of abelian transitive groups of the symmetric groups?

For instance:

Let $G$ be a an abelian transitive subgroup of the symmetric group $S_n$. Why does $G$ have order $n$?

Thanks for your help!

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You mean, abelian subgroups of $S_n$ that act transitively on $\{1,\ldots,n\}$? – Arturo Magidin Apr 4 '12 at 19:26
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A transitive group action is the same as the coset action on some subgroup. For that action to be faithful, the subgroup in question can contain no normal subgroups. Now think about what G being abelian means. – Steve D Apr 4 '12 at 19:29

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