Character theory of finite groups
type: Item
instance of: scholarly article
title: Character theory of finite groups
zbMATH Open document ID: 0932.20007
author: Bertram Huppert
published in: De Gruyter Expositions in Mathematics
publication date: 1998-09-03T00:00:00Z
review text: In Bull. Am. Math. Soc. 36(1999), pp. 489-492, \textit{I. M. Isaacs} has given a referat on this book of Huppert's. He welcomes it as a very good addition to the existing literature on character theory. Huppert himself mentions that his book can be seen as an addition to the (well-known) book of \textit{I. M. Isaacs}, published in 1976 under the same title (Zbl 0337.20005), and also to the book of \textit{O. Manz} and \textit{Th. Wolf} [Representations of solvable groups (1993; Zbl 0928.20008)]. In Isaacs' referat a wealth of features of the book has been mentioned; therefore this reviewer sees it now as his task to bring up some new items about the contents of the book. To the reviewer the appearance of the book came as a total surprise, certainly due to the fact that Huppert published already his famous triology around the years 1967 and 1982, and because other people, like Isaacs, Wolf and Manz, Collins (to mention a few) dealt with the subject of characters of finite groups. Don't forget also Karpilovsky's mega-work. Thus why publish a(nother) book on character theory? In the years 1973 and 1974 Huppert gave a series of lectures on the subject for students in Mainz. The contents were bundeled in an unofficial edition, in three small volumes, by the Mainzer Mathematics Institute. There was certainly a strong wish from group theorists in making these notes more public. It never happened that way. The reviewer could not find in the book under review a reference to those ``little 3-fold blue books'', but he assumes that this book is a (final?) compliance to the wish mentioned above. Of course things have been brought up to date and also added. Indeed, in the last two or three decades character theory has started to blossom intensively by work of several representation theorists. Let us look at the contents. There are 46 so-called sections. About 18 of them are introductory but very eluminating and complete (for instance, groups of order \(p^aq^b\), Frobenius groups,…
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20-02
Mathematics Subject Classification ID: 20Cxx
Mathematics Subject Classification ID: 20-01
zbMATH DE Number: 1196056
zbMATH Keywords: character degrees
zbMATH Keywords: characters of finite groups
zbMATH Keywords: induced characters
zbMATH Keywords: character correspondences
zbMATH Keywords: Clifford theory
zbMATH Keywords: projective representations
zbMATH Keywords: \(\pi\)-characters
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1196056