Definition:Group Theory/Historical Note

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