Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-17T22:18:36.941Z Has data issue: false hasContentIssue false
  • English
  • Français

On group rings of finite metabelian groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

G. Karpilovsky
G. Karpilovsky
Affiliation:
Department of Mathematics La Trobe UniversityBundoora 3083, Australia
Rights & Permissions [Opens in a new window]

Abstract

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 proved that a finite metabelian group G is determined by its group ring KG where the ring K satisfies the following conditions.

MSC classification

Secondary: 20C05: Group rings of finite groups and their modules
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 3 , November 1979 , pp. 378 - 384
Copyright
Copyright © Australian Mathematical Society 1979

References

Berman, S. D. (1955), ‘On the equation xm= 1 in an integral group ring’, Ukrain. Mat. Ž. 7, 253–261.Google Scholar
Berman, S. D. and Rossa, A. R. (1966), ‘Integral group rings of finite and periodic groups’, Algebra and Math. Logic, Izdat Kiev, Univ. Kiev, 44–53.Google Scholar
Miller, G. A., Blichfeldt, H. F. and Dickson, L. E. (1961), Theory and applications of finite groups (Dover Publications, New York).Google Scholar
Obayashi, T. (1970), ‘Integral group rings of finite groups’, Osaka J. Math., 253–256.Google Scholar
Saksonov, A. I. (1971), ‘Group rings of finite groups I’, Publ. Math. Debrecen, 18, 187–209.Google Scholar
Sehgal, S. K. (1970), ‘Isomorphism of p-adic group rings’, J. Number Theory 2, 500–508.CrossRefGoogle Scholar
Weller, W. R. (1972), The units of the integral group ring ZD4 (Thesis, Pennsylvania State University).Google Scholar
Whitcomb, A. (1968), The group ring problem (PhD Thesis, University of Chicago).Google Scholar