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)

“Evil is committed without effort, naturally, fatally; goodness is always the product of some art.”
—Charles Baudelaire (1821–1867)

“The diversity in the faculties of men, from which the rights of property originate, is not less an insuperable obstacle to a uniformity of interests. The protection of these faculties is the first object of government.”
—James Madison (1751–1836)