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

Associativity:
(a*b)*c = a*(b*c)
if a, b, c are in Group G

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.