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 \subset G are said to have the triple product property in G if for all elements s, s' \in S, t, t' \in T, u, u' \in U it is the case that


s's^{-1}t't^{-1}u'u^{-1} = 1 \Rightarrow s' = s, t' = t, u' = u

where 1 is the identity of G.

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

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