1 Group

In mathematics, a **group** is a set of elements combined with an operation (like addition or multiplication) that satisfies four main rules: there's an identity element that doesn't change other elements when combined; every element has an inverse that cancels it out; the operation is associative (changing grouping doesn't change the result); and the set is closed under the operation (combining two elements stays within the set). Groups are fundamental in understanding symmetry, structure, and algebraic systems, providing a way to study how elements relate and transform in a consistent, organized manner.