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| | : In a group written additively, the multiple <math>nx\!</math> is defined for every integer <math>n\!</math> by letting <math>nx = (-n)(-x)\!</math> for <math>n < 0\!</math> and proceeding the same way for <math>n \ge 0.\!</math> | | : In a group written additively, the multiple <math>nx\!</math> is defined for every integer <math>n\!</math> by letting <math>nx = (-n)(-x)\!</math> for <math>n < 0\!</math> and proceeding the same way for <math>n \ge 0.\!</math> |
| | | | |
| − | ===Table Work===
| + | ==Table Work== |
| | | | |
| | {| 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%" | | {| 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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| | | <math>\operatorname{e}</math> | | | <math>\operatorname{e}</math> |
| | |} | | |} |
| | + | |
| | + | <pre> |
| | + | Table 32.1 Scheme of a Group Multiplication Table |
| | + | * x0 ... xj ... |
| | + | x0 x0*x0 ... x0*xj ... |
| | + | ... ... ... ... ... |
| | + | xi xi*x0 ... xi*xj ... |
| | + | ... ... ... ... ... |
| | + | </pre> |
| | + | |
| | + | <pre> |
| | + | Table 32.2 Scheme of the Regular Ante-Representation |
| | + | Element Function as Set of Ordered Pairs of Elements |
| | + | x0 { <x0, x0*x0>, ..., <xj, x0*xj>, ..., } |
| | + | ... |
| | + | xi { <x0, xi*x0>, ..., <xj, xi*xj>, ..., } |
| | + | ... |
| | + | </pre> |
| | + | |
| | + | <pre> |
| | + | Table 32.3 Scheme of the Regular Post-Representation |
| | + | Element Function as Set of Ordered Pairs of Elements |
| | + | x0 { <x0, x0*x0>, ..., <xj, xj*x0>, ..., } |
| | + | ... |
| | + | xi { <x0, x0*xi>, ..., <xj, xj*xi>, ..., } |
| | + | ... |
| | + | </pre> |