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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
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Abstract

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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