# Character Theory of Finite Groups

American Mathematical Soc., 1976 - Mathematics - 303 pages
Character theory is a powerful tool for understanding finite groups. in particular, the theory has been a key ingredient in the classification of finite simple groups. Characters are also of interest in their own right, and their properties are closely related to properties of the structure of the underlying group. The book begins by developing the module theory of complex group algebras. After the module-theoretic foundations are laid in the first chapter, the focus is primarily oncharacters. This enhances the accessibility of the material for students, which was a major consideration in the writing. Also with students in mind, a large number of problems are included, many of them quite challenging. in addition to the development of the basic theory (using a cleaner notationthan previously), a number of more specialized topics are covered with accessible presentations. These include projective representations, the basics of the Schur index, irreducible character degrees and group structure, complex linear groups, exceptional characters, and a fairly extensive introduction to blocks and Brauer characters. This is a corrected reprint of the original 1976 version, later reprinted by Dover. Since 1976 it has become the standard reference for character theory,appearing in the bibliography of almost every research paper in the subject. It is largely self-contained, requiring of the reader only the most basic facts of linear algebra, group theory, Galois theory and ring and module theory.

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### Contents

 Group representations and characters 13 Characters and integrality 33 Products of characters 47 Induced characters 62 Normal subgroups 78 T I sets and exceptional characters 99 Brauers theorem 126 Changing the field 144
 The Schur index 160 Projective representations 174 Character degrees 198 Character correspondence 219 Linear groups 240 Changing the characteristic 262 Appendix Some character tables 287 Copyright

### References from web pages

Review: I. Martin Isaacs, Character theory of finite groups
I. Martin Isaacs, Character theory of finite groups. Pure and Applied Math., Academic Press, New York, San Francisco, and London, 1976, xii + 303 pp., ...
projecteuclid.org/ handle/ euclid.bams/ 1183539464

Representation Theory of Groups - Teoria della Rappresentazione ...
im Isaacs,Character theory of finite groups. Corrected reprint of the 1976 original; S. Lang, Algebra; jp Serre, Répresentations Linéaires des Groupes Finis ...
www.math.unipd.it/ ~carnoval/ rappre.html

On the field of character values of finite solvable groups
[4] im isaacs, Character Theory of Finite Groups. New York 1976. [5] im ISAACS, Primitive Characters, Normal Subgroups, and M-Groups. Math. Z. 177, 267-284 ...

On the theory of equations in finite groups
[8] im Isaacs, Character theory of finite groups, Academic Press, New York 1976. [9] G. Karpilovsky, Structure of blocks of group algebras,Longman, ...
www.iop.org/ EJ/ article/ 1064-5632/ 59/ 6/ A08/ IZV_59_6_A08.pdf

Springer Online Reference Works
[11], im Isaacs, "Character theory of finite groups" , Acad. Press (1976). [12], M. Aschbacher, "Finite group theory" , Cambridge Univ. Press (1986) ...
eom.springer.de/ F/ f040270.htm

Character Theory of Finite Groups I. Martin Isaacs Publication Year: 2006 ISBN-10: 0-8218-4229-3 ISBN-13: 978-0-8218-4229-4 AMS Chelsea Publishing , vol. ...
www.ams.org/ bookpages/ chel-359/

JSTOR: A Note on the Non-Existence of Regular Bases for Finite Groups
im Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976. 5. G. James and M. Liebeck, Representations and Characters of Groups, ...

Zentralblatt MATH Database 1931 – 2008 0903.20004
Isaacs’ excellent book on ordinary character theory [Character theory of finite groups. (1976; Zbl 0337.20005)]. In the introduction the author expresses ...
zmath.impa.br/ cgi-bin/ zmen/ ZMATH/ en/ zmath.html?first=1& maxdocs=3& type=pdf& rv=J+B+Olsson& format=complete

A note on character degrees of finite groups
Character theory of finite groups (Academic Press, 1976). [2] im Isaacs. Large orbits in actions of nilpotent groups. Proc. Amer. Math. Soc. 127 ...
www.atypon-link.com/ WDG/ doi/ abs/ 10.1515/ jgth.2004.003

Navarro: Characters and the generalized Fitting subgroup
[3] im Isaacs , Character theory of finite groups, Academic Press , New York , 1976 . MR 460423 | Zbl 0337.20005. Copyright Cellule mathdoc 2005 | Crédit ...
www.numdam.org/ numdam-bin/ fitem?id=RSMUP_1988__80__83_0