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

by Hans Wussing, Abraham Shenitzer (Translator)

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.

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

Genres: Mathematics

272 pages, Hardcover

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.