‎"CAYLEY, ARTHUR.‎
‎On the Theory of Groups, as depending on the Symbolic Equation thetan=1. - [THE THEORY OF GROUPS]‎

‎London, Taylor & Francis, 1854. 8vo. Bound in contemporary half calf with gilt lettering and five raised bands in gilt to spine. In ""Philosophical Magazine"", Fourth Series, Vol. 7. 1854. Wear to extremities and stamp to title-page. Otherwise fine and clean. Pp. 40-47. (Entire volume: VII, (1), 536 pp. + 4 engraved plates.)‎

Reference : 47094

‎First edition The first abstract definition and treatment of the concept of a group. Lagrange and Galois had, among others, already used group theoretic methods for solving polynomial equations"" however, they considered only particular examples of groups, e.g., roots. It was Cayley, who first gave an abstract definition of groups as a collection of symbols equipped with an operation. In this paper he also proved that every group is isomorphic to a group of permutations, i.e. Cayley's Theorem, and he introduced the so called ""Cayley Tables"". ‎