Genesis of the Abstract Group Concept: A Contribution to the History of the Origin of Abstract Group Theory
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Genesis of the Abstract Group Concept: A Contribution to the History of the Origin of Abstract Group Theory

by Hans Wussing
     
 

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This informative survey chronicles the process of abstraction that ultimately led to the axiomatic formulation of the abstract notion of group. Hans Wussing, former Director of the Karl Sudhoff Institute for the History of Medicine and Science at Leipzig University, contradicts the conventional thinking that the roots of the abstract notion of group lie

Overview


This informative survey chronicles the process of abstraction that ultimately led to the axiomatic formulation of the abstract notion of group. Hans Wussing, former Director of the Karl Sudhoff Institute for the History of Medicine and Science at Leipzig University, contradicts the conventional thinking that the roots of the abstract notion of group lie strictly in the theory of algebraic equations. Wussing declares their presence in the geometry and number theory of the late eighteenth and early nineteenth centuries.
This survey ranges from the works of Lagrange via Cauchy, Abel, and Galois to those of Serret and Camille Jordan. It then turns to Cayley, to Felix Klein's Erlangen Program, and to Sophus Lie, concluding with a sketch of the state of group theory circa 1920, when the axiom systems of Webber were formalized and investigated in their own right.
"It is a pleasure to turn to Wussing's book, a sound presentation of history," observed the Bulletin of the American Mathematical Society, noting that "Wussing always gives enough detail to let us understand what each author was doing, and the book could almost serve as a sampler of nineteenth-century algebra. The bibliography is extremely good, and the prose is sometimes pleasantly epigrammatic."

Product Details

ISBN-13:
9780486458687
Publisher:
Dover Publications
Publication date:
05/11/2007
Series:
Dover Books on Mathematics Series
Pages:
336
Sales rank:
854,886
Product dimensions:
6.00(w) x 9.10(h) x 0.80(d)

Meet the Author

Hans Wussing is director of the Karl Sudhoff Institute for the History of Medicine and Science at Karl Marx University in Leipzig, Germany.

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