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MyWikiBiz, Author Your Legacy — Monday December 23, 2024
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By way of collecting a short-term pay-off for all the work &mdash; not to mention all the peirce-spiration &mdash; that we sweated out over the regular representations of the Klein 4-group <math>V_4,\!</math> let us write out as quickly as possible in ''relative form'' a minimal budget of representations of the symmetric group on three letters, <math>S_3 = \operatorname{Sym}(3).</math>  After doing the usual bit of compare and contrast among these divers representations, we will have enough concrete material beneath our abstract belts to tackle a few of the presently obscur'd details of Peirce's early "Algebra + Logic" papers.
 
By way of collecting a short-term pay-off for all the work &mdash; not to mention all the peirce-spiration &mdash; that we sweated out over the regular representations of the Klein 4-group <math>V_4,\!</math> let us write out as quickly as possible in ''relative form'' a minimal budget of representations of the symmetric group on three letters, <math>S_3 = \operatorname{Sym}(3).</math>  After doing the usual bit of compare and contrast among these divers representations, we will have enough concrete material beneath our abstract belts to tackle a few of the presently obscur'd details of Peirce's early "Algebra + Logic" papers.
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{| align="center" cellpadding="6" width="90%"
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| align="center" |
 
<pre>
 
<pre>
 
Table 1.  Permutations or Substitutions in Sym {A, B, C}
 
Table 1.  Permutations or Substitutions in Sym {A, B, C}
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o---------o---------o---------o---------o---------o---------o
 
o---------o---------o---------o---------o---------o---------o
 
</pre>
 
</pre>
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|}
    
Writing this table in relative form generates the following natural representation of <math>S_3.\!</math>
 
Writing this table in relative form generates the following natural representation of <math>S_3.\!</math>
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