Prékopa–Leindler inequality: Difference between revisions
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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. 438–449. | |||
==See also== | |||
[[Category:Finite groups|*]] | |||
[[Category:Properties of groups]] |
Latest revision as of 17:45, 20 April 2013
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.