Abstract Algebra/Group Theory/Group/Definition of a Group/Definition of Associativity



=Definition of Associativity= Let G be a group with binary operation $$\ast$$


 * $$ \forall \; a, b, c \in G: (a \ast b) \ast c = a \ast (b \ast c) $$

=Usage=
 * 1) If a, b, c are in G, (a $$\ast$$ b) $$\ast$$ c = a $$\ast$$ (b $$\ast$$ c)

=Notice=
 * 1) G has to be a group
 * 2) All of a, b and c have to be elements of G.
 * 3) $$\ast$$ has to be the binary operation of G
 * 4) The converse is not necessary true:
 * a (a $$\ast$$ b) $$\ast$$ c = a $$\ast$$ (b $$\ast$$ c) does not mean a, b or c must be in G.