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Math Help - Permutations

  1. #1
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    Permutations

    In S_4, find a cyclic subgroup of order 4 and a non-cyclic one as well.


    Let a and b belong to S_n. Prove that bab^-1 and a are both even or both odd.
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  2. #2
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    Quote Originally Posted by Juancd08 View Post
    In S_4, find a cyclic subgroup of order 4 and a non-cyclic one as well.
    V = \{(1), (12)(34),(13)(24),(14)(23)\}.
    And \left< (1234) \right> are such examples.

    Let a and b belong to S_n. Prove that bab^-1 and a are both even or both odd.
    Hint: If a=(a_1,...,a_k) then bab^{-1} = (b(a_1),...,b(a_k)).
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