Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-25T22:00:43.697Z Has data issue: false hasContentIssue false
  • English
  • Français

On the radical of the group algebra of a p-nilpotent group

Published online by Cambridge University Press:  09 April 2009

R. J. Clarke
R. J. Clarke
Affiliation:
Mathematics Department University of Adelaide
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we give a basis for the radical of the group algebra of a p-nilpotent group over a field of characteristic p in terms of the ordinary representation theory of the group. We use our result to calculate the exponent of the radical for such a group.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 1 , February 1972 , pp. 119 - 123
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Curtis, C. W. and Reiner, I., Representation Theory of Finite Groups and Associative Algebras (New York 1962).Google Scholar
[2]Higman, D. G., ‘On modules with a group of operators’, Duke Math. J. 21 (1954), 369–376.CrossRefGoogle Scholar
[3]Srinivasan, B., ‘On the indecomposable representations of a certain class of groups’, Proc. London Math. Soc. 10 (1960), 497–513.CrossRefGoogle Scholar
[4]Villamayor, O. E., ‘On the semisimplicity of group algebras II’, Proc. Amer. Math. Soc. 10 (1959), 27–31.Google Scholar