Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-20T15:31:34.115Z Has data issue: false hasContentIssue false
  • English
  • Français

Integral Group Rings Without Proper Units

Published online by Cambridge University Press:  20 November 2018

K. Hoechsmann  and
S.K. Sehgal
K. Hoechsmann
Affiliation:
University of British Columbia Vancouver
S.K. Sehgal
Affiliation:
University of Alberta Edmonton Canada
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.

If A is an elementary abelian ρ-group and C one of its cyclic subgroups, the integral group rings ZA contains, of course, the ring ZC. It will be shown below, for A of rank 2 and ρ a regular prime, that every unit of ZA is a product of units of ZC, as C ranges over all cyclic subgroups.

Keywords

Primary 20C05Secondary 16A2516A18
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 1 , 01 March 1987 , pp. 36 - 42
Copyright
Copyright © Canadian Mathematical Society 01

References

1. Borevich, Z. and Shafarewich, I., Number Theory, Academic Press, N.Y., 1966.Google Scholar
2. Cliff, G., Sehgal, S. and Weiss, A., Units of Integral Group Rings of Metabelian Groups, J. Alg., 73(1981).Google Scholar
3. Curtis, C. and Reiner, I., Representation theory of finite groups and associative algebras, Interscience, N.Y., 1962.Google Scholar
4. Hasse, H., Vorlesungen über Klassenkorper theorie, Physica-Verlag, Wurzburg (1967).Google Scholar
5. Hoechsmann, K., Sehgal, S. and Weiss, A., Cyclotomic Units and the Unit Group of an Elementary Abelian Group Ring, Archiv d. Math, (to appear).Google Scholar
6. Hoechsmann, K., Functions on Finite Vector Spaces and Units in Abelian Group Rings, Can. Math. Bull, (to appear).Google Scholar
7. Kervaire, M. and Murthy, M., On the projective class group of cyclic groups of prime power order, Comm. Math. Helvet., 52 (1977), pp. 415–452.Google Scholar
8. Lang, S., Cyclotomic Fields, Springer-Verlag, N.Y., 1978.Google Scholar
9. Sehgal, S., Topics in Group Rings, Dekker, N.Y., 1978.Google Scholar