Triple Product Property

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


s's^{-1}t't^{-1}u'u^{-1} = 1 \Rightarrow s' = s, t' = t, u' = u

where is the identity of .

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

Famous quotes containing the words triple, product and/or property:

    The triple pillar of the world transformed
    Into a strumpet’s fool.
    William Shakespeare (1564–1616)

    [The political mind] is a strange mixture of vanity and timidity, of an obsequious attitude at one time and a delusion of grandeur at another time. The political mind is the product of men in public life who have been twice spoiled. They have been spoiled with praise and they have been spoiled with abuse.
    Calvin Coolidge (1872–1933)

    The awareness of the all-surpassing importance of social groups is now general property in America.
    Johan Huizinga (1872–1945)