# Order set-determined group

From Groupprops

*This group property is about the given group being determined, upto isomorphism, by certain statistic(s)*

## Definition

A finite group is said to be **order set-determined** if given any other group such that:

- and have the same order (i.e. total cardinality)
- The set of orders of elements of is the same as the set of orders of elements of

then must be isomorphic to .