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13. Let a, b be elements of some group G with |a|=m and |b|=n.Show that if...

13. Let a, b be elements of some group G with |a|=m and |b|=n.Show that if gcd(m,n)=1 then <a> union <b>={e}.
18. Let G be a group that has at least two elements and has no non-trivial subgroups. Show that G is cyclic of prime order.
20. Let A be some permutation in Sn. Show that A^2 is in An.

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