# Triple product property

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

Let be a non-trivial group. Three nonempty subsets are said to have the *triple product property* in if for all elements , , it is the case that

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

## References

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