In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms.Groups recur throughout mathematics, and the methods of …

In mathematics, a group is a set equipped with an operation that combines any two elements of the set to produce a third element of the set, in such a way that the operation is associative, an identity element exists and every element has an inverse.These three conditions, called group axioms, hold for number systems and many other mathematical structures.