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:

    “And we fairies, that do run
    By the triple Hecate’s team
    From the presence of the sun,
    Following darkness like a dream,
    Now are frolic. Not a mouse
    Shall disturb this hallowed house.”
    —William Shakespeare (1564–1616)

    “Good is a product of the ethical and spiritual artistry of individuals; it cannot be mass-produced.”
    —Aldous Huxley (1894–1963)

    “The second property of your excellent sherris is the warming
    of the blood.”
    —William Shakespeare (1564–1616)