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.

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. 438–449.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.