Right quotient of a subset

Definition with symbols
Given a subset $$S$$ of a group $$G$$, the right quotient of $$S$$, denoted as $$SS^{-1}$$, is defined as the set of all elements that can be written as $$ab^{-1}$$ where $$a$$ and $$b$$ are both in $$S$$.

A subset of a group equals its right quotient if and only if it is a subgroup.