Hostname: page-component-cc8bf7c57-l9twb Total loading time: 0 Render date: 2024-12-11T22:10:19.222Z Has data issue: false hasContentIssue false
  • English
  • Français

Group algebras of some generalised soluble groups

Published online by Cambridge University Press:  20 January 2009

R. P. Knott
R. P. Knott
Affiliation:
Department of Mathematics, Sheffield Polytechnic
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 (8) Stonehewer referred to the following open question due to Amitsur: If G is a torsion-free group and F any field, is the group algebra, FG, of G over F semi-simple? Stonehewer showed the answer was in the affirmative if G is a soluble group. In this paper we show the answer is again in the affirmative if G belongs to a class of generalised soluble groups

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 1 , June 1972 , pp. 1 - 5
Copyright
Copyright © Edinburgh Mathematical Society 1972

References

REFERENCES

(1) Amitsur, S. A., On the semi-simplicity of group algebras, Michigan Math. J. 6 (1959), 251–253.CrossRefGoogle Scholar
(2) Bovdi, A. A., Group rings of torsion-free groups, Sibirsk. Mat. Z. 1 (1960), 555–558.Google Scholar
(3) Hall, P., On non-strictly simple groups, Proc. Cambridge Phil. Soc. 59 (1963), 531–553.CrossRefGoogle Scholar
(4) Kurosh, A. G., The Theory of Groups (Chelsea, New York, 1960).Google Scholar
(5) Mal'cev, A. I., Nilpotent torsion-free groups, Izv. Akad. Nauk. USSR Ser. Mat. 13 (1949), 201–212.Google Scholar
(6) Neumann, B. H., On ordered groups, Amer. J. Math. 71 (1949), 1–18.Google Scholar
(7) Plotkin, B. I., Radical groups, Mat. Sb. N. S. 37 (79) (1955), 507–526:Google Scholar
Transl. Amer. Math. Soc. (2) 17 (1961), 9–28.Google Scholar
(8) Stonehewer, S. E., Group algebras of some torsion-free groups J. Algebra 13 (1969), 143–147.CrossRefGoogle Scholar
(9) Villamayor, O. E., On the semi-simplicity of group algebras II, Proc. Amer. Math. Soc. 10 (1959), 27–31.Google Scholar
(10) Wallace, D. A. R., The radical of the group algebra of a subgroup, of a polycyclic group and of a restricted SN-group, Proc. Edinburgh Math. Soc. 17 (II) (1970), 165–171.Google Scholar