Discrete Mathematics: Prove that a group of order 3 must be a cyclic group.

It is proved that the group of order 3 must be cyclic;

Let the group be G, then 1∈G, let a∈G and a≠ 1, then ord(a) | ord(G)=3 and ord(a)≠ 1, so ORD (A) =

It is proved that there are only two kinds of 4-order groups in the sense of isomorphism:

Let the group be G, because ord(G)=4=2*2=4* 1, so let a∈G and a≠ 1, there must be ord(a)=2 or 4.

If order(a)= 4, then G =

I hope you can understand.