Abelian groups

An Abelian group is a mathematical structure where a set of elements can be combined using an operation—like addition—that follows specific rules: the operation is associative (order of grouping doesn’t matter), there's an identity element (a neutral element that doesn't change other elements when combined), each element has an inverse (a complement that cancels it out), and importantly, the operation is commutative (the order of elements doesn't matter). Think of simple addition of numbers: no matter the order, the sum stays the same. Abelian groups provide a foundation for studying symmetry, number theory, and many areas of mathematics.