# Definition:Group Theory

(Redirected from Definition:Theory of Substitutions)

Jump to navigation
Jump to search
## 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