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Math Help - Alternating Group A5

  1. #1
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    Alternating Group A5

    Prove that A5 is a group of order 60 having no subgroup of order 30.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by johnt4335 View Post
    Prove that A5 is a group of order 60 having no subgroup of order 30.
    Have you covered the fact that A_5 is simple yet? As if so, you can apply the fact that a subgroup of order 30 would have index 2, and so is normal, a contradiction.

    Otherwise, I am sorry but I can't think of a neat way of doing it. I keep wanting to prove that A_5 is simple...
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