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Klein four-group

535 bytes added, 21:43, 2 January 2008
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==Definition==
 
===Verbal definitions===
The Klein-four group is defined in the following equivalent ways:
* It is the unique non-cyclic group of order 4
* It is the subgroup of [[symmetric group:S4|the symmetric group on 4 elements]] comprising the double transpositions, and the identity element.
 
===Multiplication table===
 
{| class="wikitable" border="1"
! Element !! <math>e</math> !! <math>a</math> !! <math>b</math> !! <math>c</math>
|-
|<math>e</math> || <math>e</math> || <math>a</math> || <math>b</math> || <math>c</math>
|-
|<math>a</math> || <math>a</math> || <math>e</math> || <math>c</math> || <math>b</math>
|-
|<math>b<math> || <math>b</math> || <math>c</math> || <math>e</math> || <math>a</math>
|-
|<math>c</math> || <math>c</math> || <math>b</math> || <matH>a</math> || <math>e</math>
|}
==Group properties==
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