Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T07:15:26.778Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks on the commutativity of the radicals of group algebras

Published online by Cambridge University Press:  18 May 2009

Shigeo Koshitani
Shigeo Koshitani
Affiliation:
Department of Mathematics, Tsukuba University, Sakura-mura, Ibaraki 300–31, Japan
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.

Let K be an arbitrary field with characteristic p > 0, G a finite group of order pag′ with (p, g′) = 1, P a p-Sylow subgroup of G and G′ the commutator subgroup of G. For a ring R denote by J(R) the Jacobson radical of R and by Z(R) the centre of R. We write KG for the group algebra of G over K.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 20 , Issue 1 , January 1979 , pp. 63 - 68
Copyright
Copyright © Glasgow Mathematical Journal Trust 1979

References

REFERENCES

1.Brauer, R. and Nesbitt, C., On the modular characters of groups, Ann. of Math. 42 (1941), 556–590.CrossRefGoogle Scholar
2.Dornhoff, L., Group representation theory (part B), (Dekker, 1972).Google Scholar
3.Hamernik, W., Group structure and properties of block ideals of the group algebra, Glasgow Math. J. 16 (1975), 22–28.CrossRefGoogle Scholar
4.Michler, G. O., Blocks and centers of group algebras, in Lectures on rings and modules, Lecture Notes in Mathematics 246 (Springer-Verlag, 1972), 429–563.CrossRefGoogle Scholar
5.Morita, K., On group rings over a modular field which possess radicals expressible as principal ideals, Sci. Rep. of Tokyo Bunrika Daigaku A 4 (1951), 177–194.Google Scholar
6.Osima, M., On primary decomposable group rings, Proc. Phys.-Math. Soc. Japan 24 (1942), 1–9.Google Scholar
7.Passman, D. S., Radicals of twisted group rings, Proc. London Math. Soc. (3) 20 (1970), 409–437.CrossRefGoogle Scholar
8.Wallace, D. A. R., Note on the radical of a group algebra, Proc. Cambridge Philos. Soc. 54 (1958), 128–130.CrossRefGoogle Scholar
9.Wallace, D. A. R., Group algebras with central radicals, Proc. Glasgow Math. Assoc. 5 (1962), 103–108.CrossRefGoogle Scholar
10.Wallace, D. A. R., Group algebras with radicals of square zero, Proc. Glasgow Math. Assoc. 5 (1962), 158–159.CrossRefGoogle Scholar
11.Wallace, D. A. R., On the commutativity of the radical of a group algebra, Proc. Glasgow Math. Assoc. 7 (1965), 1–8.CrossRefGoogle Scholar