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Group axioms
A quantity of G of elementsA, B, C... is a group, if
1. between the items a linkage ("multiplication " called) is avowed, so that per is assigned two to items A and B unique an item C of the quantity of G (C is called " product " of A and B, C = AB ],
2. this multiplication the associative law fulfills: (AB)C = A(BC),
3. in G an item E (one element) exists, so that to all items A applies to the quantity of G: AE = E A = A,
4. it to each item A from the quantity of G an inverse item X in G gives, so that AX = XA -- E; with the designation X = A l applies: AA l = A -1 A = E. |
A group is called abelsche or commutative group, if to the multiplication that applies commutatively:
AB = B A
Continue please with step 148 !
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