Klein four-group

Mathematical abelian group

In mathematics, the Klein four-group is an abelian group with four elements, in which each element is self-inverse and in which composing any two of the three non-identity elements produces the third one. It can be described as the symmetry group of a non-square rectangle, as the group of bitwise exclusive-or operations on two-bit binary values, or more abstractly as , the direct product of two copies of the cyclic group of order 2 by the Fundamental Theorem of Finitely Generated Abelian Groups. It was named Vierergruppe, meaning four-group) by Felix Klein in 1884. It is also called the Klein group, and is often symbolized by the letter or as .

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