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)

“Everything that is beautiful and noble is the product of reason and calculation.”
—Charles Baudelaire (1821–1867)

“By avarice and selfishness, and a groveling habit, from which none of us is free, of regarding the soil as property, or the means of acquiring property chiefly, the landscape is deformed, husbandry is degraded with us, and the farmer leads the meanest of lives. He knows Nature but as a robber.”
—Henry David Thoreau (1817–1862)