Triple product property

In abstract algebra, the triple product property is an identity satisfied in some groups.
Let formula_1 be a non-trivial group. Three nonempty subsets formula_2 are said to have the "triple product property" in formula_1 if for all elements formula_4, formula_5, formula_6 it is the case that
where formula_8 is the identity of formula_1.
It plays a role in research of fast matrix multiplication algorithms.