The study of groups arose early in the nineteenth century originally a group was a set of permutations with the property that the combination of any two permutations again belongs to the set. subsequently, this definition was generalised to the concept of an abstract group which was defined to be a set.
Not necessarily of permutations, together with a method of combining its elements that is subject to a few simple laws. group theory plays an important part in present-day mathematics and science.
Definition and Examples of Group Theory
What is group theory?
Group theory is the branch of abstract algebra used to study and combine abstract concepts consisting of symmetry. This is the tool used to determine symmetry. Also, symmetry operations and symmetry components are two basic and influential concepts in group theory.
What is the meaning of group theory?
Group theory, in modern algebra, is the study of groups, which are systems consisting of a set of elements and a binary operation that can be applied to two elements of a set, which together meet certain axes.