View source for Prékopa–Leindler inequality

In [[abstract algebra]], the '''triple product property''' is an identity satisfied in some [[group (mathematics)|groups]].

Let <math>G</math> be a non-trivial group.  Three nonempty subsets <math>S, T, U \subset G</math> are said to have the ''triple product property'' in <math>G</math> if for all elements <math>s, s' \in S</math>, <math>t, t' \in T</math>, <math>u, u' \in U</math> it is the case that

: <math>
s's^{-1}t't^{-1}u'u^{-1} = 1 \Rightarrow s' = s, t' = t, u' = u
</math>

where <math>1</math> is the identity of <math>G</math>.

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

==References==

* Henry Cohn, Chris Umans. A Group-theoretic Approach to Fast Matrix Multiplication. {{arxiv|math.GR/0307321}}. ''Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science'', 11–14 October 2003, Cambridge, MA, IEEE Computer Society, pp.&nbsp;438&ndash;449.

==See also==

[[Category:Finite groups|*]]
[[Category:Properties of groups]]