The Development and Understanding of the Concept of Quotient Group
HISTORIA MATHEMATICA 20 (1993), 68-88 The Development and Understanding of the Concept of Quotient Group JULIA NICHOLSON Merton College, Oxford University, Oxford OXI 4JD, United Kingdom This paper describes the way in which the concept of quotient group was discovered and developed during the 19th century, and examines possible reasons for this development. The contributions of seven mathematicians in particular are discussed: Galois, Betti, Jordan, Dedekind, Dyck, Frobenius, and H61der. The important link between the development of this concept and the abstraction of group theory is considered. © 1993 AcademicPress. Inc. Cet article decrit la d6couverte et le d6veloppement du concept du groupe quotient au cours du 19i~me si~cle, et examine les raisons possibles de ce d6veloppement. Les contributions de sept math6maticiens seront discut6es en particulier: Galois, Betti, Jordan, Dedekind, Dyck, Frobenius, et H61der. Le lien important entre le d6veloppement de ce concept et l'abstraction de la th6orie des groupes sera consider6e. © 1993 AcademicPress, Inc. Diese Arbeit stellt die Entdeckung beziehungsweise die Entwicklung des Begriffs der Faktorgruppe wfihrend des 19ten Jahrhunderts dar und untersucht die m/)glichen Griinde for diese Entwicklung. Die Beitrfi.ge von sieben Mathematikern werden vor allem diskutiert: Galois, Betti, Jordan, Dedekind, Dyck, Frobenius und H61der. Die wichtige Verbindung zwischen der Entwicklung dieses Begriffs und der Abstraktion der Gruppentheorie wird betrachtet. © 1993 AcademicPress. Inc. AMS subject classifications: 01A55, 20-03 KEY WORDS: quotient group, group theory, Galois theory I. INTRODUCTION Nowadays one can hardly conceive any more of a group theory without factor groups... B. L. van der Waerden, from his obituary of Otto H61der [1939] Although the concept of quotient group is now considered to be fundamental to the study of groups, it is a concept which was unknown to early group theorists.
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