Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-12-04T09:22:53.604Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Structure of Group Algebras, I

Published online by Cambridge University Press:  20 November 2018

James A. Cohn  and
Donald Livingstone
James A. Cohn
Affiliation:
University of Michigan
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.

With this paper we begin a study of the structure of the group algebra RG of a finite group G over the ring of algebraic integers R in an algebraic number field k. The basic question is whether non-isomorphic groups can have isomorphic algebras over R. We shall show that this is impossible if G is

  • (a) abelian,

  • (b) Hamiltonian,

  • (c) one of a special class of p-groups.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 583 - 593
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Berman, S. D., On certain properties of integral group rings, Dokl. Akad. Nauk SSSR (n.s.), 91 (1953), 7–9.Google Scholar
2. Cohn, J. A. and Livingstone, D., On groups of order p3 Can. J. Math., 15 (1963), 622–624.Google Scholar
3. Coleman, D. B., Finite groups with isomorphic group algebras, Trans. Amer. Math. Soc, 105 (1962), 1–8.Google Scholar
4. Higman, G., The units of group rings, Proc. London Math. Soc, 46 (1940), 231–248.Google Scholar
5. Mann, H. B., Introduction to algebraic number theory (Columbus, 1955).Google Scholar
6. Perlis, S. and Walker, G., Abelian group algebras of finite order, Trans. Amer. Math. Soc, 68 (1950), 420–426.Google Scholar