# 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

- 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 $9$

- 2008: Paul Halmos and Steven Givant:
*Introduction to Boolean Algebras*... (previous) ... (next): $\S 1$: Exercise $5$ - 2010: Steve Awodey:
*Category Theory*(2nd ed.) ... (previous) ... (next): $\S 1.5$: Definition $1.4$