Abelian group

An Abelian group is a mathematical structure where a set of elements is combined using an operation (like addition or multiplication) that satisfies four key properties: closure (the result stays within the set), associativity (grouping of operations doesn't matter), an identity element (a special element that doesn't change others when combined), and inverses (each element has a counterpart that cancels it out). Additionally, it's commutative, meaning the order of the elements doesn't affect the result. This makes Abelian groups a fundamental concept in algebra, useful for studying symmetry, number systems, and various mathematical and scientific applications.