In mathematical structures, there are among other things : groups.
Among their particular properties of the group, the groups have the property of associativity.Within the various groups, there are commutative (abelian) and non commutative (non-abelian) groups.
Why is there a hierarchy of interest between associativity and commutativity in groups ; that is , why do we assume that groups are associative, while commutativity is only an "option" ?(why is associativity "more important" than commutativity ?)
Are there algebra structures which don't assume associativity ?
