This is my question: Prove that there is no subgroup with size 6 in the symmetric group $A_4$.
What i thought is that $A_4$ has all the 2,4 circles,a subgroup with order 6 must be cyclic so there is no element in $A_6$ with order 6 so there is no subgroup with size 6.
I want to be sure that I am right,
thanks.
