Torsion group

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.

The exponent of a periodic group G is the least common multiple, if it exists, of the orders of the elements of G. Any finite group has an exponent: it is a divisor of |G|.