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Math Help - Suppose |G|=22. Show G has elements of order 2 and 11.

  1. #1
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    Suppose |G|=22. Show G has elements of order 2 and 11.

    Suppose G is a group of size 22. Show that G contains an element of order 2 and an element of order 11.

    Thanks for any replies.
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  2. #2
    Senior Member Tinyboss's Avatar
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    This is Cauchy's theorem. The proof isn't too hard, and is included in most texts. McKay gave a really beautiful one that's outlined in the exercises in Dummit & Foote.

    Edit: I just checked, and McKay's proof is the one given on the Wikipedia page. http://en.wikipedia.org/wiki/Cauchy'...(group_theory)
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