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

Revision as of 02:32, 26 April 2012

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→‎6.6. Basic Notions of Group Theory: format table

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<~~pre~~>

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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%"

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Table 34.2 Regular Representation of the Group Z4(.)

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|+ <math>\text{Table 34.2}~~\text{Regular Representation of the Group}~Z_4(\cdot)</math>

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Element Function as Set of Ordered Pairs of Elements

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|- style="height:50px"

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1 { <1, 1>, <a, a>, <b, b>, <c, c> }

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| style="border-bottom:1px solid black; border-right:1px solid black" | <math>\text{Element}\!</math>

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a { <1, a>, <a, b>, <b, c>, <c, 1> }

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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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b { <1, b>, <a, c>, <b, 1>, <c, a> }

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|- style="height:50px"

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c { <1, c>, <a, 1>, <b, a>, <c, b> }

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| width="20%" style="border-right:1px solid black" | <math>\operatorname{1}</math>

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<~~/pre~~>

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| width="4%" | <math>\{\!</math>

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| width="16%" | <math>(\operatorname{1}, \operatorname{1}),</math>

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| width="20%" | <math>(\operatorname{a}, \operatorname{a}),</math>

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| width="20%" | <math>(\operatorname{b}, \operatorname{b}),</math>

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| width="16%" | <math>(\operatorname{c}, \operatorname{c})</math>

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| width="4%" | <math>\}\!</math>

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|- style="height:50px"

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| style="border-right:1px solid black" | <math>\operatorname{a}</math>

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| <math>\{\!</math>

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| <math>(\operatorname{1}, \operatorname{a}),</math>

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| <math>(\operatorname{a}, \operatorname{b}),</math>

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| <math>(\operatorname{b}, \operatorname{c}),</math>

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| <math>(\operatorname{c}, \operatorname{1})</math>

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| <math>\}\!</math>

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|- style="height:50px"

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| style="border-right:1px solid black" | <math>\operatorname{b}</math>

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| <math>\{\!</math>

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| <math>(\operatorname{1}, \operatorname{b}),</math>

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| <math>(\operatorname{a}, \operatorname{c}),</math>

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| <math>(\operatorname{b}, \operatorname{1}),</math>

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| <math>(\operatorname{c}, \operatorname{a})</math>

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| <math>\}\!</math>

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|- style="height:50px"

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| style="border-right:1px solid black" | <math>\operatorname{c}</math>

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| <math>\{\!</math>

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| <math>(\operatorname{1}, \operatorname{c}),</math>

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| <math>(\operatorname{a}, \operatorname{1}),</math>

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| <math>(\operatorname{b}, \operatorname{a}),</math>

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| <math>(\operatorname{c}, \operatorname{b})</math>

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| <math>\}\!</math>

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|}

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<br>

<pre>

Jon Awbrey

12,089

edits