Tensor product

The term tensor product is used in a wide variety of contexts:

• Tensor product of abelian groups is the most common usage.
• Tensor product of groups (not necessarily abelian), also called the non-abelian tensor product, is a related idea.
• Tensor product of Lie rings is another related idea.
• Tensor product of vector spaces is a (non-group theoretic) object but has applications in group theory where vector spaces arise, e.g. linear representation theory.