Question

Help on the following 4 true/false question.
1) The rotation of a siheral group form a cyclic subgroup.
2)A subgroup of a cyclic group is a cyclic
3)A subset H of a group is a subgroup if a and b belong to H implies that ab^-1 belong to H.
4) If A is a 21 cycle in S50, the order of A is 21.

I personally thinking is all true.

However I am not confident, can someone double check for me.