The Foundation Period in the History of Group Theory (Classic Reprint)

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Excerpt from The Foundation Period in the History of Group TheoryHenri Poincare/has pointed out that the fundamental concep tion of a group is evident in Euclid's work, in fact that the foun dation of Euclid's demonstrations is the group idea.(1) Poincare establishes this assertion by showing that such operations as suc cessive superposition and rotation about a fixed axis presuppose the displacements of a group. He shows that the axioms of Euclid Which are easily referred to the group concept are those omitted in Euclids work, and that those axioms Which may be referred to the groupxcon cept with more difficulty, are the axioms explicitly enunciated. However much the fundamental group notions are dormant in the work of early mathematicians, it was not until the latter part of the eight eenth century that these notions began to take life and develop. The period of foundation of group theory as a distinct science extends from Lagrange (1770) to Cauchy (lsmm - é) a period of about seventy five years. We find Lagrange considering the number of values a ra tional function can assume when the variables are permuted in every possible way. With this beginning the development may be traced down through the contributions of Vandermonde, Ruffini, Abbati, Abel, Galois, Bertrand, and Hermite to Cauchy's period of active production (lsnm-l846). Group theory was at the beginning of the period a dis covery useful in the consideration of the theory of equations, at the end it existed as a distinct science, not yet, to be sure, eh tirely freed from the restrictions of applications to other branches but sufficiently so that this may be considered the close of the foundation period. In the first part of this paper we shall_consid~.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.