Definition:Group Theory

Definition

Group theory is a branch of abstract algebra which studies groups and other related algebraic structures.

Also see

• Results about group theory can be found here.

Historical Note

The field of group theory was initiated by Évariste Galois as a consequence of his work on establishing the general solubility criteria of polynomials in radicals.

Group theory was originally called the theory of substitutions until Arthur Cayley's $1854$ paper On the theory of groups in which he introduced the concept of the abstract group.

Nowadays group theory permeates most of modern algebra, and has important applications in such fields as crystallography and quantum mechanics.

Sources

• 1967: John D. Dixon: Problems in Group Theory ... (next): Preface
• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Group Theory