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Opposite Group
In group theory, a branch of mathematics, an opposite group is a way to construct a group from another group that allows one to define right action as a special case of left action. Monoids, groups, rings, and algebras can be viewed as categories with a single object. The construction of the opposite category generalizes the opposite group, opposite ring, etc. Definition Let G be a group under the operation *. The opposite group of G, denoted G^, has the same underlying set as G, and its group operation \mathbin is defined by g_1 \mathbin g_2 = g_2 * g_1. If G is abelian, then it is equal to its opposite group. Also, every group G (not necessarily abelian) is naturally isomorphic In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition of morphisms) of the categories involved. Hence, a natur ... to its opposite group: An isomorphism \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Opposite Group Nature
Opposite or Opposites may refer to: * Opposite (semantics), a word that means the reverse of a word * Opposite (leaf), an arrangement of leaves on a stem * Opposite (mathematics), the negative of a number; numbers that, when added, yield zero *"The Opposite", a 1994 episode of ''Seinfeld'' Music * The Opposites, Dutch rap group * Opposites (album), ''Opposites'' (album), 2013 album by Scottish alternative rock band Biffy Clyro ** Opposite (song), "Opposite" (song), 2013 song by Biffy Clyro * Opposites (EP), ''Opposites'' (EP), 2010 album by Tracey Thorn *"The Opposite", 1964 song by Johnny Burnette See also * Opposite hitter, a position in volleyball * Antinomy, opposites in a certain form from Kant * * Anti (other) * Contrary (other) * Flipside (other) * Inverse (other) * Opposite sex (other) * Opposition (other) * Polar opposite (other) * The House Opposite (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
