Definitions
1.NounAny group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:
Any (often, but not necessarily, abelian) group whose binary operation is called addition.
Any of certain algebraic objects (ring, field or vector space, etc., whose definition includes a commutative operation called addition) regarded as a group under addition.
Any group object (such as a group functor, group scheme, etc.), whose binary operation is called addition.
2.NounAny (often, but not necessarily, abelian) group whose binary operation is called addition.
3.NounAny of certain algebraic objects (ring, field or vector space, etc., whose definition includes a commutative operation called addition) regarded as a group under addition.
4.NounAny group object (such as a group functor, group scheme, etc.), whose binary operation is called addition.