Torsion group
Group in which each element has finite order / From Wikipedia, the free encyclopedia
"Periodic group" redirects here. For groups in the chemical periodic table, see Group (periodic table).
In group theory, a branch of mathematics, a torsion group or a periodic group is a group in which every element has finite order. The exponent of such a group, if it exists, is the least common multiple of the orders of the elements.
For example, it follows from Lagrange's theorem that every finite group is periodic and it has an exponent that divides its order.