👉 Group theory, a fundamental branch of abstract algebra, studies the symmetries of mathematical objects through the lens of groups. A group is a set equipped with an operation (like addition or multiplication) that satisfies four key properties: closure, associativity, the existence of an identity element, and the existence of inverse elements for each member. These groups can be finite or infinite and are used to describe symmetries in various contexts, from geometric transformations (like rotations and reflections) to algebraic structures (such as permutations of sets). Group theory provides a powerful framework for understanding and classifying symmetries, playing a crucial role in fields like physics, chemistry, and computer science.
