The Genesis of the Abstract Group Concept

Preface Preface to the American Edition Translator's Note Introduction Part I. Implicit Group-Theoretic Ways of Thinking in Geometry and Number Theory 1. Divergence of the different tendencies inherent in the evolution of geometry during the first half of the nineteenth century 2. The search for ordering principles in geometry through the study of geometric relations (geometrische Verwandtschaften) 3. Implicit group theory in the domain of number theory: The theory of forms and the first axiomatization of the implicit group concept Part II. Evolution of the Concept of a Group as a Permutation Group 1. Discovery of the connection between the theory of solvability of algebraic equations and the theory of permutations 2. Perfecting the theory of permutations 3. The group-theoretic formulation of the problem of solvability of algebraic equations 4. The evolution of the permutation-theoretic group concept 5. The theory of permutation groups as an independent and far-reaching area of investigation Part III. Transition of the Concept of a Transformation Group and the Development of the Abstract Group Concept 1. The theory of invariants as a classification tool in geometry 2. Group-theoretic classification of geometry: The Erlangen Program of 1872 3. Groups of geometric motions; Classification of transformation groups 4. The shaping and axiomatization of the abstract group concept Epilogue Notes Bibliography Name Index Subject Index