The development and understanding of the concept of quotient group
type: Item
instance of: scholarly article
title: The development and understanding of the concept of quotient group
zbMATH Open document ID: 0767.01022
author: Julia Nicholson
published in: Historia Mathematica
publication date: 1993-05-16T00:00:00Z
review text: The author traces the emergence of the notions of normal subgroup and quotient group from Galois to Hölder and emphasizes the essential role of the development of the abstract notion of equivalence classes of Dedekind and Cantor. [The author is quite correct in sticking to the development of abstract group theory from the theory of substitution groups; Klein's development of geometry from transformation groups played no role in the general development of group theory since he used invariant theory as his only tool].
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 20-03
zbMATH DE Number: 168476
zbMATH Keywords: normal subgroup
zbMATH Keywords: Galois
zbMATH Keywords: Hölder
zbMATH Keywords: Dedekind
zbMATH Keywords: Cantor
zbMATH Keywords: substitution groups
zbMATH Keywords: transformation groups
reviewed by: Heinrich Guggenheimer
MaRDI profile type: Publication
full work available at URL: hmat.1993.1007
OpenAlex ID: W2039416400
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DOI: 10.1006/HMAT.1993.1007
description: scientific article; zbMATH DE number 168476