267 Abelian Group

A set with a binary operation under which the order of combining two elements does not change the result that is used to define addition of vectors.

definition (Abelian Group) A group with axioms (1) to (4) and the following additional condition:

• (Commutativity) \(a * b = b * a\)

where

• \((G, *)\) is a group.
• \(a, b \in G\) are elements of the group.

• Abelian Group
• Antisymmetry
• Binary Operations
• Field
• Group
• Group Theory
• Homomorphism
• Integral Domain
• Permutational Antisymmetry
• Ring
• Symmetry