The Genesis of the Abstract Group Concept: A Contribution to the History of the Origin of Abstract Group Theory
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."
What people are saying - Write a review
We haven't found any reviews in the usual places.
Divergence of the dhTerent tendencies inherent in the evolution
13 other sections not shown
Other editions - View all
Abel abstract group concept abstract group theory algebraic equations algebraische algébrique Betti Cauchy Cayley Cayley's commutative complete composition Comptes rendus Paris congruence connection continuous groups coordinates d'une definition degré deux differential equations Disquisitiones arithmeticae elements équations equations of degree Erlangen Program finite groups formulation fundamental Galois theory Galois's Gauss given Gleichungen group of permutations group theory group-theoretic Gruppe Gruppen historical ideas infinite invariant theory investigations isomorphism Jordan Journ Klein Kronecker Kronecker's Lagrange Lie's line geometry Liouville Math mathematical mathematicians Mathematik Memoire methods metric Mobius nombre noneuclidean geometry number theory Operationen operations paper permutation groups permutation theory permutation-theoretic group concept problem projective geometry proof properties quantic rational functions relations roots Ruffini Serret solution solvability of algebraic space structure subgroup substitutions theorem theory of algebraic theory of equations theory of permutation tion transformation groups Transformationen unendlich variables Vorlesungen Wussing Zahlen zwei