Characters of finite groups. Volume 1
type: Item
instance of: scholarly article
title: Characters of finite groups. Volume 1
zbMATH Open document ID: 1426.20002
DOI: 10.1515/9783110224078
author: Yakov Berkovich
author: Lev Kazarin
author: Emmanuel M. Zhmud'
published in: De Gruyter Expositions in Mathematics
publication date: 2017-12-11T00:00:00Z
review text: According to \textit{C. W. Curtis} [Pioneers of representation theory: Frobenius, Burnside, Schur, and Brauer. Providence, RI: American Mathematical Society; London: London Mathematical Society (1999; Zbl 0939.01007)], the year 1897 was the centennial of two events in the history of mathematics: The publication of the first paper on representation of finite groups by Frobenius and the appearance of the first treatise in English of the theory of finite groups by Burnside. Burnside soon developed his own approach to representations of finite groups and Frobenius together with Burnside explored the new subject and its application to finite group theory. They were soon joined with Schur and a few years later by Brauer, who are called the pioneers of representation theory of finite groups. The importance of this theory appear in proving fundamental properties of finite groups, such as the existence of a Frobenius kernel in Frobenius groups which is proved using representation theory and still there is no group theoretrical proof for it. This theory is still developing and many new concepts are emerging. Character theory over the complex field is associated to representation theory and proving group theoretical properties uses characters, rather than representations. The aim of the book under review is to place character theory and its applications to finite groups within the reach of graduate students with a modest knowledge of group theory and linear algebra. Although the books by \textit{I. M. Isaacs} [Character theory of finite groups. New York-San Francisco-London: Academic Press, a subsidiary of Harcourt Brace Jovanovich, Publishers. (1976; Zbl 0337.20005)], \textit{B. Huppert} [Character theory of finite groups. Berlin: Walter de Gruyter (1998; Zbl 0932.20007)] and \textit{W. Feit} [The representation theory of finite groups. Amsterdam - New York - Oxford: North-Holland Publishing Company. (1982; Zbl 0493.20007)] focus on character theory with applications, but the…
reviewed by: M. R. Darafsheh
Mathematics Subject Classification ID: 20-02
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 6816972
zbMATH Keywords: character theory
zbMATH Keywords: representation theory.
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1515/9783110224078
OpenAlex ID: W2478069152
Recommended article: Characters of finite groups. Volume 2
Recommended article: On characters of finite groups
Recommended article: Character theory of finite groups
Recommended article: Q3840441
Recommended article: Q4871631
Recommended article: Q3413656
Recommended article: Q4387775
Recommended article: The Characters of the Finite General Linear Groups
Recommended article: Characters of groups associated with finite algebras
Recommended article: Q4201905
description: scientific article; zbMATH DE number 6816972