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Revision as of 03:08, 10 June 2009
, 03:08, 10 June 2009→Note 18: markup
Line 3,373:
Line 3,373:
| <e, e, e>
−| <e, f, f>
−| <e, g, g>
−| <e, h, h>
−|
−| <f, e, f>
−| <f, f, e>
−| <f, g, h>
−| <f, h, g>
−|
−| <g, e, g>
−| <g, f, h>
−| <g, g, e>
−| <g, h, f>
−|
−| <h, e, h>
−| <h, f, g>
−| <h, g, f>
−| <h, h, e>
−
In the case of <math>V_4 = (G, \cdot),</math> where <math>G\!</math> is the ''underlying set'' <math>\{ \operatorname{e}, \operatorname{f}, \operatorname{g}, \operatorname{h} \},</math> we have the 3-adic relation <math>L(V_4) \subseteq G \times G \times G</math> whose triples are listed below:
In the case of <math>V_4 = (G, \cdot),</math> where <math>G\!</math> is the ''underlying set'' <math>\{ \operatorname{e}, \operatorname{f}, \operatorname{g}, \operatorname{h} \},</math> we have the 3-adic relation <math>L(V_4) \subseteq G \times G \times G</math> whose triples are listed below:
+
+{| align="center" cellpadding="6" width="90%"
+| align="center" |
+<math>\begin{matrix}
+(\mathrm{e}, \mathrm{e}, \mathrm{e}) &
+(\mathrm{e}, \mathrm{f}, \mathrm{f}) &
+(\mathrm{e}, \mathrm{g}, \mathrm{g}) &
+(\mathrm{e}, \mathrm{h}, \mathrm{h})
+\\[6pt]
+(\mathrm{f}, \mathrm{e}, \mathrm{f}) &
+(\mathrm{f}, \mathrm{f}, \mathrm{e}) &
+(\mathrm{f}, \mathrm{g}, \mathrm{h}) &
+(\mathrm{f}, \mathrm{h}, \mathrm{g})
+\\[6pt]
+(\mathrm{g}, \mathrm{e}, \mathrm{g}) &
+(\mathrm{g}, \mathrm{f}, \mathrm{h}) &
+(\mathrm{g}, \mathrm{g}, \mathrm{e}) &
+(\mathrm{g}, \mathrm{h}, \mathrm{f})
+\\[6pt]
+(\mathrm{h}, \mathrm{e}, \mathrm{h}) &
+(\mathrm{h}, \mathrm{f}, \mathrm{g}) &
+(\mathrm{h}, \mathrm{g}, \mathrm{f}) &
+(\mathrm{h}, \mathrm{h}, \mathrm{e})
+\end{matrix}</math>
+|}
<pre>
<pre>
−It is part of the definition of a group that the 3-adic
It is part of the definition of a group that the 3-adic
relation L c G^3 is actually a function L : G x G -> G.
relation L c G^3 is actually a function L : G x G -> G.
