Finite group theory

Finite group theory studies mathematical structures called groups, which consist of a set of elements and an operation combining them, where this operation satisfies properties like closure, associativity, identity, and inverses. In finite groups, the set has a limited number of elements. These structures help understand symmetry and patterns across mathematics and sciences. For example, they can describe how an object can be rotated or reflected without changing its core shape. Finite group theory provides tools to classify and analyze these symmetrical structures, revealing fundamental properties in areas like chemistry, physics, and cryptography.