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

by Hans Wussing

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."

Genres: Mathematics

336 pages, Paperback

First published May 16, 1984

About the author

Hans-Ludwig Wußing (October 15, 1927 in Waldheim – April 26, 2011 in Leipzig) was a German historian of mathematics and science. Wussing is the author of numerous scientific historical publications, the author of many mathematicians' biographies, and co-editor of several series of publications, including biographies in the Teubner Verlag, and several volumes in the series Klassiker der exakten Wissenschaften (Ostwald's Classics of the Exact Sciences), in particular on Euler's work on functional theory, Gauss's diary, and Felix Klein's Erlangen program. In 1993 he was awarded the Kenneth O. May Prize.