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)

“Man’s main task in life is to give birth to himself, to become what he potentially is. The most important product of his effort is his own personality.”
—Erich Fromm (1900–1980)

“Abscond. To “move” in a mysterious way, commonly with the property of another.”
—Ambrose Bierce (1842–1914)