“On the theory of groups, as depending on the symbolic equation theta^n=1.” From Philosophical Magazine, Fourth Series, Vol. 7, pp. 40-47

London: Taylor & Francis, 1854. FIRST PRINTING. Bound into boards, label with author and title in gilt on front cover. An excellent copy. First edition of Cayley’s groundbreaking work on identification of groups. This work contained a number of invaluable insights and provided mathematicians with what is now the accepted procedure for defining a group. “In the abstract theory of groups, where nothing is said of the nature of the elements, the group is completely specified if all possible products are known or determinable” (on other words a collection of symbols equipped with an operation.) He also sets forth “Cayley’s Theorem” which states that “every finite group whatsoever is isomorphic with a suitable group of permutations.”

DSB, III, pp. 162-170.