View source for Klein-4 group

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==Definition==
The ''Klein-4 [[group]]'' ({{AKA}}: ''Viergruppe''{{rAAPAG}}), {{M|1=V_4=\{1,a,b,c\} }} is a group on 4 elements with the operation {{M|*:V_4\times V_4\rightarrow V_4}} defined as follows:
<center>
{| class="wikitable" border="1"
|-
| style="text-align:center;" |<m>
\begin{array}{|c|cccc|}
\hline
V_4 & 1 & a & b & c \\\hline
1 & 1 & a & b & c \\
a & a & 1 & c & b \\
b & b & c & 1 & a \\
c & c & b & a & a \\\hline
\end{array}</m>
|-
! Operator tables for the ''Klien-4 group''
|}
</center>
Recall that to calculate the product say, {{M|a*b}} we look at the row corresponding to {{M|a}} and find the entry in the {{M|b}} column, which is {{M|c}} here (the same as {{M|b*a}}, so be sure you're doing it the correct way)
: '''Claim: ''' this is indeed a group.
==References==
<references/>
{{Group theory navbox|plain}}
{{Definition|Abstract Algebra|Group Theory}}