The History of Combinatorial Group Theory: A Case Study in the History of IdeasSpringer Science & Business Media, 6 de des. 2012 - 234 pàgines 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. |
Altres edicions - Mostra-ho tot
The History of Combinatorial Group Theory: A Case Study in the History of Ideas Bruce Chandler,Wilhelm Magnus Visualització de fragments - 1982 |
The History of Combinatorial Group Theory: A Case Study in the History of Ideas B. Chandler,W. Magnus Previsualització no disponible - 1982 |
The History of Combinatorial Group Theory: A Case Study in the History of Ideas B. Chandler,W. Magnus Previsualització no disponible - 2011 |
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abelian group algebraic number appeared ARTIN automorphisms B. H. NEUMANN BAER BAUMSLAG BURNSIDE BURNSIDE's problem called Chapter coefficients combinatorial group theory commutator complex concept construction contains coset countable defining relations DEHN DEHN's denote discontinuous groups DYCK equations exists extensions fact finite groups finite number finitely generated groups finitely presented group formulated free group free product freely reduced FRICKE and KLEIN fundamental group fundamental region geometric given graph group G group-theoretical HILBERT important infinite cyclic integers introduced isomorphic knot KUROSH large number later Lie groups Lie ring linear groups literature lower central series LYNDON and SCHUPP MAGNUS manifolds mapping Math mathematicians matrices mentioned metabelian groups method monograph NIELSEN normal subgroup number theory one-relator groups p-groups paper Ph.D POINCARE prime number proof proved quotient group REIDEMEISTER SCHREIER solvable solvable groups space theorem theory of finite theory of groups TIETZE tion topic topological word problem