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:

    “Their martyred blood and ashes sow
    O’er all the Italian fields where still doth sway
    The triple tyrant; that from these may grow
    A hundredfold, who, having learnt thy way,
    Early may fly the Babylonian woe.”
    —John Milton (1608–1674)

    “...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)

    “To throw obstacles in the way of a complete education is like putting out the eyes; to deny the rights of property is like cutting off the hands. To refuse political equality is like robbing the ostracized of all self-respect, of credit in the market place, of recompense in the world of work, of a voice in choosing those who make and administer the law, a choice in the jury before whom they are tried, and in the judge who decides their punishment.”
    —Elizabeth Cady Stanton (1815–1902)