Abstract Algebra/Group Theory/Group/Definition of a Group/Definition of Associativity
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Definition of Associativity
- If a, b, c are in G, (a b) c = a (b c)
- G has to be a group
- All of a, b and c have to be elements of G.
- has to be the binary operation of G
- The converse is not necessary true:
- a (a b) c = a (b c) does not mean a, b or c must be in G.