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

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- Mar 14th 2011, 01:44 PMfeyomiSuppose |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. - Mar 14th 2011, 01:49 PMTinyboss
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)