Triple product property

In abstract algebra, the triple product property is an identity satisfied in some groups.

Let G be a non-trivial group. Three nonempty subsets S , T , U ⊂ G are said to have the triple product property in G if for all elements s , s ′ ∈ S , t , t ′ ∈ T , u , u ′ ∈ U it is the case that

where 1 is the identity of G .

It plays a role in research of fast matrix multiplication algorithms.