Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-17T17:19:40.927Z Has data issue: false hasContentIssue false
  • English
  • Français

Group Algebras With Central Radicals

Published online by Cambridge University Press:  18 May 2009

D. A. R. Wallace
D. A. R. Wallace
Affiliation:
The University, Glasgow
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.

It is well known that when the characteristic p(≠ 0) of a field divides the order of a finite group, the group algebra possesses a non-trivial radical and that, if p does not divide the order of the group, the group algebra is semi-simple. A group algebra has a centre, a basis for which consists of the class-sums. The radical may be contained in this centre; we obtain necessary and sufficient conditions for this to happen.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 5 , Issue 3 , January 1962 , pp. 103 - 108
Copyright
Copyright © Glasgow Mathematical Journal Trust 1962

References

1.Brauer, R. and Nesbitt, C., On the modular characters of groups, Ann. of Math. (2) 42 (1941), 556–590.CrossRefGoogle Scholar
2.Feit, W., On the structure of Frobenius groups, Canad. J. Math. 9 (1957), 587–596.CrossRefGoogle Scholar
3.Higman, G., Groups and rings having automorphisms without trivial fixed elements, J.London Math. Soc. 32 (1957), 321–334.CrossRefGoogle Scholar
4.Jennings, S. A., The structure of the group ring of a p-group over a modular field, Trans. Amer. Math. Soc. 50 (1941), 175–185.Google Scholar
5.Thompson, J., Finite groups with fixed-point-free automorphisms of prime order, Proc. Nat. Acad.Sci. 45(1959), 578–581.CrossRefGoogle ScholarPubMed
6.Thompson, J., Normals-complements for Finite Groups, Math. Z. 72 (1960), 332–354.CrossRefGoogle Scholar
7.Wallace, D., Note on the radical of a group algebra, Proc. Cambridge Philos. Soc. 54 (1958), 128–130.CrossRefGoogle Scholar
8.Zassenhaus, H., The theory of groups (2nd edition, New York, 1958).Google Scholar