The Genesis of the Abstract Group Concept - by Hans Wussing (Paperback)

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.

Book Synopsis

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."

Review Quotes

"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)