Book contents
- Frontmatter
- Contents
- Preface
- Twenty-five years of Groups St Andrews Conferences
- Original Introduction
- 1 An elementary introduction to coset table methods in computational group theory
- 2 Applications of cohomology to the theory of groups
- 3 Groups with exponent four
- 4 The Schur multiplier: an elementary approach
- 5 A procedure for obtaining simplified defining relations for a subgroup
- 6 GLn and the automorphism groups of free metabelian groups and polynomial rings
- 7 Isoclinisms of group extensions and the Schur multiplicator
- 8 The maximal subgroups of the Chevalley group G2(4)
- 9 Generators and relations for the cohomology ring of Janko's first group in the first twenty one dimensions
- 10 The Burnside group of exponent 5 with two generators
- 11 The orientability of subgroups of plane groups
- 12 On groups with unbounded non-archimedean elements
- 13 An algorithm for the second derived factor group
- 14 Finiteness conditions and the word problem
- 15 Growth sequences relative to subgroups
- 16 On the centres of mapping class groups of surfaces
- 17 A glance at the early history of group rings
- 18 Units of group rings: a short survey
- 19 Subgroups of small cancellation groups: a survey
- 20 On the hopficity and related properties of some two-generator groups
- 21 The isomorphism problem and units in group rings of finite groups
- 22 On one-relator groups that are free products of two free groups with cyclic amalgamation
- 23 The algebraic structure of ℵ0-categorical groups
- 24 Abstracts
- 25 Addendum to: “An elementary introduction to coset table methods in computational group theory”
- 26 Addendum to: “Applications of cohomology to the theory of groups”
- 27 Addendum to: “Groups with exponent four”
- 28 Addendum to: “The Schur multiplier: an elementary approach”
17 - A glance at the early history of group rings
Published online by Cambridge University Press: 07 September 2010
- Frontmatter
- Contents
- Preface
- Twenty-five years of Groups St Andrews Conferences
- Original Introduction
- 1 An elementary introduction to coset table methods in computational group theory
- 2 Applications of cohomology to the theory of groups
- 3 Groups with exponent four
- 4 The Schur multiplier: an elementary approach
- 5 A procedure for obtaining simplified defining relations for a subgroup
- 6 GLn and the automorphism groups of free metabelian groups and polynomial rings
- 7 Isoclinisms of group extensions and the Schur multiplicator
- 8 The maximal subgroups of the Chevalley group G2(4)
- 9 Generators and relations for the cohomology ring of Janko's first group in the first twenty one dimensions
- 10 The Burnside group of exponent 5 with two generators
- 11 The orientability of subgroups of plane groups
- 12 On groups with unbounded non-archimedean elements
- 13 An algorithm for the second derived factor group
- 14 Finiteness conditions and the word problem
- 15 Growth sequences relative to subgroups
- 16 On the centres of mapping class groups of surfaces
- 17 A glance at the early history of group rings
- 18 Units of group rings: a short survey
- 19 Subgroups of small cancellation groups: a survey
- 20 On the hopficity and related properties of some two-generator groups
- 21 The isomorphism problem and units in group rings of finite groups
- 22 On one-relator groups that are free products of two free groups with cyclic amalgamation
- 23 The algebraic structure of ℵ0-categorical groups
- 24 Abstracts
- 25 Addendum to: “An elementary introduction to coset table methods in computational group theory”
- 26 Addendum to: “Applications of cohomology to the theory of groups”
- 27 Addendum to: “Groups with exponent four”
- 28 Addendum to: “The Schur multiplier: an elementary approach”
Summary
INTRODUCTION
Group rings usually appear in courses on group representation theory as a means to gain a broader view of the subject and connect it to the general theory of algebras and their representations (e.g. Boerner or Curtis & Reiner). This may suggest the misleading idea that it was precisely this point of view that motivated the definition and study of group rings. In fact, this is explicitly stated by several authors who attribute the idea to E. Noether.
Though both topics are closely related and representation theory was actually a motivation for much of the work done in group rings, the historical order of development was rather the reverse: interest in the structure of group rings led to the discovery of some of the earlier theorems on group representations. This fact was pointed out in a most interesting paper by T. Hawkins but, perhaps due to the fact that it was published in a journal devoted to the history of science rather than to mathematics itself, it seems to have remained unnoticed by those working on the subject. Recent books and surveys fail to credit either A. Cayley or T. Molien, and some still attribute to E. Noether the creation of the theory, omitting even the influence of R. Brauer.
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- Information
- Groups - St Andrews 1981 , pp. 270 - 280Publisher: Cambridge University PressPrint publication year: 1982