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Math Help - [SOLVED] Cylic and a non cyclic subgroup in the Permutation group S(4)

  1. #1
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    [SOLVED] Cylic and a non cyclic subgroup in the Permutation group S(4)

    I am stuck with this problem.

    In S_4, find a cyclic subgroup of order 4 and a noncyclic subgroup of order 4.

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by akolman View Post
    I am stuck with this problem.

    In S_4, find a cyclic subgroup of order 4 and a noncyclic subgroup of order 4.

    Thanks in advance.
    < (1 2 3 4) > and Klein four-group.
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  3. #3
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    Quote Originally Posted by akolman View Post
    I am stuck with this problem.

    In S_4, find a cyclic subgroup of order 4 and a noncyclic subgroup of order 4.

    Thanks in advance.
    For non-cyclic take V=\{ (12)(34),(13)(24),(14)(23), \text{id} \}.
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