Triple product property

Triple product property

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

Let G be a non-trivial finite 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 implies s' = s, t' = t, u' = u

where 1 is the identity of G.

References

* Henry Cohn, Chris Umans. A Group-theoretic Approach to Fast Matrix Multiplication. arXiv|archive=math.GR|id=0307321. "Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science", 11-14 October 2003, Cambridge, MA, IEEE Computer Society, pp. 438–449.

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