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

Let $G$ be a an abelian transitive subgroup of the symmetric group $S_n$. Show that $G$ has order $n$.

Thanks for your help!

  • 1
    You mean, abelian subgroups of $S_n$ that act transitively on $\{1,\ldots,n\}$?2012-04-04
  • 3
    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.2012-04-04
  • 0
    Anon, How can you show that: Every subgroup of Sn acts faithfully on {1, 2, ..., n}. Thank you.2014-12-26

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