Thread: 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.

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)