Just as with monoids, we often talk about a group G
without mentioning all binary and unary operations.
Sometimes we
indicate with a single word what type of operation we are considering.
For example, the additive group of the integers is understood to be the group defined on the monoid (Z,+,0), whose inverse map is z -> -z.
Most properties that we have derived for monoids so far, also hold for groups. Similarly, notation introduced for monoids will also apply to groups. For example, a group is called commutative (or abelian after the mathematician Abel) if the corresponding monoid is commutative, i.e., the multiplication is commutative.