# Definition:Group Theory/Historical Note

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## Historical Note on Group Theory

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

- 1854:
*On the theory of groups, as depending on the symbolic equation $\theta^n - 1$*(*Phil. Mag.***Ser. 4****Vol. 7**: pp. 40 – 47) - 1971: Allan Clark:
*Elements of Abstract Algebra*... (previous) ... (next): Introduction - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**group** - 2008: David Joyner:
*Adventures in Group Theory*(2nd ed.) ... (previous) ... (next): Where to begin... - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**group**