I have read that a cyclic group G is one that can be generated by a single element a called the generator , aϵG. While looking up Wikipedia for Torsion Groups(periodic groups), I found:
"In group theory, a branch of mathematics, a torsion group or a periodic group is a group in which each element has finite order. All finite groups are periodic. The concept of a periodic group should not be confused with that of a cyclic group."
I am confused, after this I couldn't find a satisfying difference between the two(periodic and cyclic groups).