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)

    A product of the untalented, sold by the unprincipled to the utterly bewildered.
    Al Capp (1909–1979)

    For wisdom is the property of the dead,
    A something incompatible with life; and power,
    Like everything that has the stain of blood,
    A property of the living; but no stain
    Can come upon the visage of the moon
    When it has looked in glory from a cloud.
    William Butler Yeats (1865–1939)