Skip to main content Accessibility help
A Course in Finite Group Representation Theory
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 3
  • Export citation
  • Recommend to librarian
  • Buy the print book

Book description

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.


'This is a well-written and motivated book, with carefully chosen topics, examples and exercises to engage the reader, making it suitable in the classroom or for self-study.'

Felipe Zaldivar Source: MAA Reviews

'The author aims to provide a comprehensive but fastpaced grounding in results which can be applied to areas as diverse as number theory, combinatorics, topology or commutative algebra … While the proofs are rigorous, the style is relatively informal and designed to showcase as many results as possible which are applicable beyond the realms of \"pure representation theory.'

Stuart Martin Source: MathSciNet

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Send to Kindle
  • Send to Dropbox
  • Send to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.


[1] J. L., Alperin, Diagrams for modules, J. Pure Appl. Algebra 16 (1980), 111–119.
[2] J. L., Alperin, Local representation theory, Cambridge Studies in Advanced Mathematics 11, Cambridge University Press, 1986.
[3] D. J., Benson, Representations and cohomology 1 and 2, Cambridge Studies in Advanced Mathematics 30 and 31, Cambridge University Press, 1998.
[4] D. J., Benson and J. F., Carlson, Diagrammatic methods for modular representations and cohomology, Comm. Algebra 15 (1987), 53–121.
[5] D. J., Benson and J. H., Conway, Diagrams for modular lattices, J. Pure Appl. Algebra 37 (1985), 111–116.
[6] N., Blackburn, On a special class of p-groups, Acta Math. 100 (1958), 45–92.
[7] S., Brenner, Modular representations of p groups, J. Algebra 15 (1970), 89–102.
[8] S., Brenner, Decomposition properties of some small diagrams of modules, Symposia Mathematica 13, 127–141, Academic Press, 1974.
[9] W. W., Crawley-Boevey, On tame algebras and bocses, Proc. London Math. Soc. 56 (1988), 451–483.
[10] C. W., Curtis and I., Reiner, Methods of representation theory, vol. I, John Wiley, New York, 1981.
[11] Yu. A., Drozd, Tame and wild matrix problems: Representations and quadratic forms (in Russian), pp. 39–74, 154, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 154 (1979), 3974 translated in Amer. Math. Soc. Transl. 128 (1986), 31–55.
[12] K., Erdmann, Blocks of tame representation type and related algebras, Lecture Notes in Mathematics 1428, Springer Verlin, 1990.
[13] W., Feit, The representation theory of finite groups, North-Holland Mathematical Library 25, North-Holland, Amsterdam, 1982.
[14] L. K., Hua, Introduction to number theory, Springer, Berlin, 1982.
[15] M., Prest, Wild representation type and undecidability, Comm. Algebra 19 (1991), 919–929.
[16] D. S., Rim, Modules over finite groups, Ann. of Math. 69 (1959), 700–712.
[17] C. M., Ringel, The representation type of local algebras, in Representations of algebras, Ottawa 1974, Lecture Notes in Mathematics 488, Springer, Berlin, 1975.
[18] C. M., Ringel, The indecomposable representations of the dihedral 2-groups, Math. Ann. 214 (1975), 19–34.
[19] R. G., Swan, Projective modules over group rings and maximal orders, Ann. Math. 76 (1962), 55–61.
[20] J. G., Thackray, Modular representations of some finite groups, Ph.D. thesis, University of Cambridge, 1981.
[21] J., Thévenaz, G-Algebras and modular representation theory, Oxford University Press, Oxford, 1995.


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.