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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)

Revision as of 14:30, 25 April 2012

1,744 bytes added ,  14:30, 25 April 2012
→‎6.6. Basic Notions of Group Theory: format table
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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>\cdot\!</math>
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| 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{e}</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{f}</math>
+
| width="20%" style="border-bottom:1px solid black" | <math>\operatorname{f}</math>
−
| width="22%" style="border-bottom:1px solid black" | <math>\operatorname{g}</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{h}</math>
+
| width="20%" 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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<br>
 
<br>
   −
<pre>
+
{| 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%"
−
Table 33.2 Regular Representation of the Group V4
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|+ <math>\text{Table 33.2}~~\text{Regular Representation of the Group}~V_4</math>
−
Element Function as Set of Ordered Pairs of Elements
+
|- style="height:50px"
−
1 { <1, 1>, <r, r>, <s, s>, <t, t> }
+
| style="border-bottom:1px solid black; border-right:1px solid black" | <math>\text{Element}\!</math>
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r { <1, r>, <r, 1>, <s, t>, <t, s> }
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| colspan="6" style="border-bottom:1px solid black" | <math>\text{Function as Set of Ordered Pairs of Elements}\!</math>
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s { <1, s>, <r, t>, <s, 1>, <t, r> }
+
|- style="height:50px"
−
t { <1, t>, <r, s>, <s, r>, <t, 1> }
+
| width="20%" style="border-right:1px solid black" | <math>\operatorname{e}</math>
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</pre>
+
| 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>
 +
|}
 +
 
 +
<br>
    
<pre>
 
<pre>
Jon Awbrey
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