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)

    ...In the past, as now, [Hollywood] was a stamping ground for tastelessness, violence, and hyperbole, but once upon a time it turned out a product which sweetened the flavor of life all over the world.
    Anita Loos (1888–1981)

    In the Greek cities, it was reckoned profane, that any person should pretend a property in a work of art, which belonged to all who could behold it.
    Ralph Waldo Emerson (1803–1882)