Definition: The term 'Abelian' means "symmetry". This concept is fundamental to both mathematics, physics and engineering. Mathematics: A group (mathematically speaking) is a set S with an operation
which satisfies some properties that are known as axioms for a group. In the case of Abelian groups, the property that we refer to as 'Symmetry' states that: For all elements x and y in G (i.e., elements in the set), if there exists an element z such that z
x = y then z
y = x. This means that every operation is commutative i.e. for every element x and y in group G, x
y = y
x In physics: The term 'Abelian' relates to symmetry of a system. For example, if you have two particles (or objects) in equilibrium, the forces acting on them are symmetric about an axis that is perpendicular to one or both of them. In engineering: - Symmetry and Abelian Group: It refers to the property of a group in which all elements commute with each other. - In the context of electronics, it also means that the output signals must be identical to the input signals. For instance, if you have two voltages V1 = 3V and V2 = -4V, their sum (V1 + V2) should equal zero. Abelian groups are fundamental in many areas of mathematics and engineering, including group theory, abstract algebra and electrical circuits. For more detailed information on Abelian Groups, please refer to the Wikipedia entry on Group Theory.

Abelian