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Home > Mathematics and Science Textbooks > Mathematics > Groups and group theory > The Genesis of the Abstract Group: Contribution to the History of the Origin of Abstract Group Theory
The Genesis of the Abstract Group: Contribution to the History of the Origin of Abstract Group Theory

The Genesis of the Abstract Group: Contribution to the History of the Origin of Abstract Group Theory


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About the Book

In this book, Hans Wussing sets out to trace the process of abstraction that led finally to the axiomatic formulation of the abstract notion of group. His main thesis is that the roots of the abstract notion of group do not lie, as frequently assumed, only in the theory of algebraic equations; they are also to be found in the geometry and the theory of numbers of the end of the 18th and the first half of the 19th centuries.The book takes us from Lagrange via Cauchy, Abel, and Galois to Serret and Camille Jordan. It then turns to Cayley, to Felix Klein's Erlangen Program, and to Sophus Lie, and ends with a sketch of the state of group theory about 1920, when the axiom systems of Webber had been formalized and investigated in their own right.

Review :
"It is a pleasure to turn to Wussing's book, a sound presentation of history .... The topic of the book is such that less is said about group theory itself than about the subjects in which it grew. These discussions are far from perfunctory; the 13 pages on Galois, for instance, are an excellent study of the spirit of his work. Wussing always gives enough detail to let us understand what each author was doing, and the book could almost serve as a sampler of 19th-century algebra. The bibliography is extremely good, and the prose is sometimes pleasantly epigrammatic."--William C. Waterhouse, "Bulletin of the American Mathematical Society" (review of the German edition)


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Product Details
  • ISBN-13: 9780262231091
  • Publisher: MIT Press Ltd
  • Publisher Imprint: MIT Press
  • Height: 229 mm
  • Spine Width: 25 mm
  • Weight: 454 gr
  • ISBN-10: 0262231093
  • Publisher Date: 16 May 1984
  • Binding: Hardback
  • Language: German
  • Sub Title: Contribution to the History of the Origin of Abstract Group Theory
  • Width: 152 mm


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