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)

    Perhaps I am still very much of an American. That is to say, naïve, optimistic, gullible.... In the eyes of a European, what am I but an American to the core, an American who exposes his Americanism like a sore. Like it or not, I am a product of this land of plenty, a believer in superabundance, a believer in miracles.
    Henry Miller (1891–1980)

    A few days later the younger son gathered all he had and traveled to a distant country, and there he squandered his property in dissolute living.
    Bible: New Testament, Luke 15:13.