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单词 Klein group
释义

Klein group

英语百科

Klein four-group

The symmetry group of this cross is the Klein four-group.  It can be flipped horizontally (a) or vertically (b) or both (ab) and remain unchanged.  Unlike a square, though, a quarter-turn rotation will change the figure.
Identity and double-transpositions of four objects form V
Other permutations of four objects, forming V as wellSee: 4 element subsets of S4

In mathematics, the Klein four-group (or just Klein group or Vierergruppe (English: four-group), often symbolized by the letter V or as K4) is the group Z2 × Z2, the direct product of two copies of the cyclic group of order 2. It was named Vierergruppe by Felix Klein in 1884. The Klein group's Cayley table is given by:

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更新时间:2025/6/21 13:49:55