Group theory began as a branch of pure mathematics. Mathematicians, through their study of the way numbers behave and how they may be treated, often discover theorems and relationships that may appear to have no immediate application to the physical...

A group is a simple mathematical system, so basic that groups appear wherever one looks in mathematics. Despite the primitive nature of a group, mathematicians have developed a rich theory about them. Specifically, a group is a mathematical system...

Group theory describes the rules of operation of sets of numbers or objects, including finite, discrete, topological, and Lie groups. Group theory became one of the central tools in elementary particle physics in the 1960s. Although quantum...

Group theory, in political science, is largely associated with Bentley and, in various reformulations, with writers on pluralism. The central argument is that societies consist of a large number of social, ethnic or economic groups, more or less...

In modern algebra, a system consisting of a set of elements and an operation for combining the elements, which together satisfy certain axioms. These require that the group be closed under the operation (the combination of any two elements produces...

In abstract algebra, group theory studies the algebraic structures known as groups. A group is a set G (the underlying set) closed under a binary operation satisfying three...