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User:Jon Awbrey/TABLE (view source)

Revision as of 14:36, 25 April 2012

372 bytes added ,  14:36, 25 April 2012
→‎Group Operation Tables
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|+ <math>\text{Table 33.1}~~\text{Multiplication Operation of the Group}~V_4</math>
 
|+ <math>\text{Table 33.1}~~\text{Multiplication Operation of the Group}~V_4</math>
 
|- style="height:50px"
 
|- style="height:50px"
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| width="12%" style="border-bottom:1px solid black; border-right:1px solid black" | <math>*\!</math>
+
| width="20%" style="border-bottom:1px solid black; border-right:1px solid black" | <math>\cdot\!</math>
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| width="22%" style="border-bottom:1px solid black" | <math>\operatorname{1}</math>
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| width="20%" style="border-bottom:1px solid black" | <math>\operatorname{e}</math>
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| width="22%" style="border-bottom:1px solid black" | <math>\operatorname{r}</math>
+
| width="20%" style="border-bottom:1px solid black" | <math>\operatorname{f}</math>
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| width="22%" style="border-bottom:1px solid black" | <math>\operatorname{s}</math>
+
| width="20%" style="border-bottom:1px solid black" | <math>\operatorname{g}</math>
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| width="22%" style="border-bottom:1px solid black" | <math>\operatorname{t}</math>
+
| width="20%" style="border-bottom:1px solid black" | <math>\operatorname{h}</math>
−
|- style="height:50px"
  −
| style="border-right:1px solid black" | <math>\operatorname{1}</math>
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| <math>\operatorname{1}</math>
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| <math>\operatorname{r}</math>
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| <math>\operatorname{s}</math>
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| <math>\operatorname{t}</math>
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|- style="height:50px"
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| style="border-right:1px solid black" | <math>\operatorname{r}</math>
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| <math>\operatorname{r}</math>
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| <math>\operatorname{1}</math>
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| <math>\operatorname{t}</math>
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| <math>\operatorname{s}</math>
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|- style="height:50px"
  −
| style="border-right:1px solid black" | <math>\operatorname{s}</math>
  −
| <math>\operatorname{s}</math>
  −
| <math>\operatorname{t}</math>
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| <math>\operatorname{1}</math>
  −
| <math>\operatorname{r}</math>
  −
|- style="height:50px"
  −
| style="border-right:1px solid black" | <math>\operatorname{t}</math>
  −
| <math>\operatorname{t}</math>
  −
| <math>\operatorname{s}</math>
  −
| <math>\operatorname{r}</math>
  −
| <math>\operatorname{1}</math>
  −
|}
  −
 
  −
<br>
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  −
{| 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>
  −
| 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="height:50px"
 
| style="border-right:1px solid black" | <math>\operatorname{e}</math>
 
| style="border-right:1px solid black" | <math>\operatorname{e}</math>
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| <math>\operatorname{f}</math>
 
| <math>\operatorname{f}</math>
 
| <math>\operatorname{e}</math>
 
| <math>\operatorname{e}</math>
 +
|}
 +
 +
<br>
 +
 +
{| 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 33.2}~~\text{Regular Representation of the Group}~V_4</math>
 +
|- style="height:50px"
 +
| style="border-bottom:1px solid black; border-right:1px solid black" | <math>\text{Element}\!</math>
 +
| colspan="6" style="border-bottom:1px solid black" | <math>\text{Function as Set of Ordered Pairs of Elements}\!</math>
 +
|- style="height:50px"
 +
| width="20%" style="border-right:1px solid black" | <math>\operatorname{e}</math>
 +
| width="4%"  | <math>\{\!</math>
 +
| width="16%" | <math>(\operatorname{e}, \operatorname{e}),</math>
 +
| width="20%" | <math>(\operatorname{f}, \operatorname{f}),</math>
 +
| width="20%" | <math>(\operatorname{g}, \operatorname{g}),</math>
 +
| width="16%" | <math>(\operatorname{h}, \operatorname{h})</math>
 +
| width="4%"  | <math>\}\!</math>
 +
|- style="height:50px"
 +
| style="border-right:1px solid black" | <math>\operatorname{f}</math>
 +
| <math>\{\!</math>
 +
| <math>(\operatorname{e}, \operatorname{f}),</math>
 +
| <math>(\operatorname{f}, \operatorname{e}),</math>
 +
| <math>(\operatorname{g}, \operatorname{h}),</math>
 +
| <math>(\operatorname{h}, \operatorname{g})</math>
 +
| <math>\}\!</math>
 +
|- style="height:50px"
 +
| style="border-right:1px solid black" | <math>\operatorname{g}</math>
 +
| <math>\{\!</math>
 +
| <math>(\operatorname{e}, \operatorname{g}),</math>
 +
| <math>(\operatorname{f}, \operatorname{h}),</math>
 +
| <math>(\operatorname{g}, \operatorname{e}),</math>
 +
| <math>(\operatorname{h}, \operatorname{f})</math>
 +
| <math>\}\!</math>
 +
|- style="height:50px"
 +
| style="border-right:1px solid black" | <math>\operatorname{h}</math>
 +
| <math>\{\!</math>
 +
| <math>(\operatorname{e}, \operatorname{h}),</math>
 +
| <math>(\operatorname{f}, \operatorname{g}),</math>
 +
| <math>(\operatorname{g}, \operatorname{f}),</math>
 +
| <math>(\operatorname{h}, \operatorname{e})</math>
 +
| <math>\}\!</math>
 
|}
 
|}
  
Jon Awbrey
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