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Revision as of 13:34, 25 April 2012
, 13:34, 25 April 2012→6.6. Basic Notions of Group Theory: format table
Table 33.1 shows the multiplication table of the group <math>V_4,\!</math> while Tables 33.2 and 33.3 present two versions of its regular representation. The first version, somewhat hastily, gives the functional representation of each group element as a set of ordered pairs of group elements. The second version, more circumspectly, gives the functional representative of each group element as a set of ordered pairs of element names, also referred to as ''objects'', ''points'', ''letters'', or ''symbols''.
Table 33.1 shows the multiplication table of the group <math>V_4,\!</math> while Tables 33.2 and 33.3 present two versions of its regular representation. The first version, somewhat hastily, gives the functional representation of each group element as a set of ordered pairs of group elements. The second version, more circumspectly, gives the functional representative of each group element as a set of ordered pairs of element names, also referred to as ''objects'', ''points'', ''letters'', or ''symbols''.
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Table 33.1 Multiplication Operation of the Group V4
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%"
|+ <math>\text{Table 33.1}~~\text{Multiplication Operation of the Group}~V_4</math>
|- style="height:50px"
| width="12%" style="border-bottom:1px solid black; border-right:1px solid black" | <math>\cdot\!</math>
| width="22%" style="border-bottom:1px solid black" | <math>\operatorname{e}</math>
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| width="22%" style="border-bottom:1px solid black" | <math>\operatorname{f}</math>
| width="22%" style="border-bottom:1px solid black" | <math>\operatorname{g}</math>
| width="22%" style="border-bottom:1px solid black" | <math>\operatorname{h}</math>
|- style="height:50px"
| style="border-right:1px solid black" | <math>\operatorname{e}</math>
| <math>\operatorname{e}</math>
| <math>\operatorname{f}</math>
| <math>\operatorname{g}</math>
| <math>\operatorname{h}</math>
|- style="height:50px"
| style="border-right:1px solid black" | <math>\operatorname{f}</math>
| <math>\operatorname{f}</math>
| <math>\operatorname{e}</math>
| <math>\operatorname{h}</math>
| <math>\operatorname{g}</math>
|- style="height:50px"
| style="border-right:1px solid black" | <math>\operatorname{g}</math>
| <math>\operatorname{g}</math>
| <math>\operatorname{h}</math>
| <math>\operatorname{e}</math>
| <math>\operatorname{f}</math>
|- style="height:50px"
| style="border-right:1px solid black" | <math>\operatorname{h}</math>
| <math>\operatorname{h}</math>
| <math>\operatorname{g}</math>
| <math>\operatorname{f}</math>
| <math>\operatorname{e}</math>
|}
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