Triple product property explained

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 thats's ^{-1} t't ^{-1} u'u ^{-1} = 1 ⇒ s' = s, t' = t, u' = u

where

1 is the identity of G .

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

References

• Henry Cohn, Chris Umans. A Group-theoretic Approach to Fast Matrix Multiplication. . Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, 11–14 October 2003, Cambridge, MA, IEEE Computer Society, pp. 438 - 449.