Definition:Group/Historical Note

Historical Note on Group

The term group was first used by Évariste Galois in $1832$, in the context of the solutions of polynomials in radicals. Augustin Louis Cauchy was also involved in this development.

The concept of the group as a purely abstract structure was introduced by Arthur Cayley in his $1854$ paper On the theory of groups.

The first one to formulate the set of axioms to define the structure of a group was Leopold Kronecker in $1870$.

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)
• 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 1.1$: Introduction
• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Introduction
• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $9$: Permutations: Summary for Chapter $9$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): group
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): group