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)

    Poetry is the only life got, the only work done, the only pure product and free labor of man, performed only when he has put all the world under his feet, and conquered the last of his foes.
    Henry David Thoreau (1817–1862)

    There is no such thing as “the Queen’s English.” The property has gone into the hands of a joint stock company and we own the bulk of the shares!
    Mark Twain [Samuel Langhorne Clemens] (1835–1910)