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Math Help - find the elements of S_4

  1. #1
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    find the elements of S_4

    I am having trouble with finding all of the elements of S_4 using cyclic notation.

    I know there are 24 elements because 4!=24, but how do I find the elements.

    Please help.
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  2. #2
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    Quote Originally Posted by mandy123 View Post
    I am having trouble with finding all of the elements of S_4 using cyclic notation.

    I know there are 24 elements because 4!=24, but how do I find the elements.

    Please help.
    Any element is a product of disjoint cycles.
    Now find all the different possibilities.

    Identity (1): \text{id}

    2-cycles (6): (12),(13),(14),(23),(24),(34)

    3-cycles (8): (123),(124),(132),(134),(142),(143),(234),(243)

    4-cycles (6): (1234),(1243),(1324),(1342),(1423),(1432)

    2-cycles times 2-cycles (3): (12)(34),(13)(24),(14)(23)
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  3. #3
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    Oh I get it now!
    Thank you so much!
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