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Field name	Details
Dewey Class	512.2
Title	The History of Combinatorial Group Theory ([EBook]) : A Case Study in the History of Ideas / by Bruce Chandler, Wilhelm Magnus.
Author	Chandler, Bruce
Added Personal Name	Magnus, Wilhelm. , 1907-1990
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 1982.
Physical Details	VIII, 234 pages : online resource.
Series	Studies in the history of mathematics and physical sciences 0172-570X ; ; 9
ISBN	9781461394877
Summary Note	One of the pervasive phenomena in the history of science is the development of independent disciplines from the solution or attempted solutions of problems in other areas of science. In the Twentieth Century, the creation of specialties witqin the sciences has accelerated to the point where a large number of scientists in any major branch of science cannot understand the work of a colleague in another subdiscipline of his own science. Despite this fragmentation, the development of techniques or solutions of problems in one area very often contribute fundamentally to solutions of problems in a seemingly unrelated field. Therefore, an examination of this phenomenon of the formation of independent disciplines within the sciences would contrib ute to the understanding of their evolution in modern times. We believe that in this context the history of combinatorial group theory in the late Nineteenth Century and the Twentieth Century can be used effectively as a case study. It is a reasonably well-defined independent specialty, and yet it is closely related to other mathematical disciplines. The fact that combinatorial group theory has, so far, not been influenced by the practical needs of science and technology makes it possible for us to use combinatorial group theory to exhibit the role of the intellectual aspects of the development of mathematics in a clearcut manner. There are other features of combinatorial group theory which appear to make it a reasona ble choice as the object of a historical study.:
Contents note	I The Beginning of Combinatorial Group Theory -- I.I Introduction to Part I -- I.2 The Foundations: Dyck’s Group-Theoretical Studies -- I.3 The Origin: The Theory of Discontinuous Groups -- I.4 Motivation: The Fundamental Groups of Topological Spaces -- I.5 The Graphical Representation of Groups -- I.6 Precursors of Later Developments -- I.7 Summary -- I.8 Modes of Communication. Growth and Distribution of Research in Group Theory -- I.9 Biographical Notes -- I.10 Notes on Terminology and Definitions -- I.11 Sources -- II The Emergence of Combinatorial Group Theory as an Independent Field -- II. 1 Introduction to Part II -- II.2 Free Groups and Their Automorphisms -- II.3 The Reidemeister—Schreier Method -- II.4 Free Products and Free Products with Amalgamations -- II.5 One-Relator Groups -- II.6 Metabelian Groups and Related Topics -- II.7 Commutator Calculus and the Lower Central Series -- II.8 Varieties of Groups -- II.9 Topological Properties of Groups and Group Extensions -- II.10 Notes on Special Groups -- II.11 Postscript: The Impact of Mathematical Logic -- II.12 Modes of Communication -- II.13 Geographical Distribution of Research and Effects of Migration -- II.14 Organization of Knowledge -- Index of Names -- Index of Subjects.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4613-9487-7
Links to Related Works	Subject References: Group theory . Group Theory and Generalizations . Mathematics . Authors: author . Chandler, Bruce . Magnus, Wilhelm. 1907-1990 . Corporate Authors: SpringerLink (Online service) . Series: Studies in the history of mathematics and physical sciences . Classification: 512.2 .

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The History of Combinatorial Group Theory: A Case Study in the History of Ideas /

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