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

# Definition of AssociativityEdit

Let G be a group with binary operation

# UsageEdit

- If
*a*,*b*,*c*are in G, (*a*b*)*c*=*a (*b**c*)

# NoticeEdit

- 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.