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Functors on Finite Vector Spaces and Units in Abelian Group Rings

Published online by Cambridge University Press:  20 November 2018

Klaus Hoechsmann
Klaus Hoechsmann*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C.
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Abstract

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If A is an elementary abelian group, let (A) denote the group of units, modulo torsion, of the group ring Z[A]. We study (A) by means of the composite

where C and B run over all cyclic subgroups and factor-groups, respectively. This map, γ, is known to be injective; its index, too, is known. In this paper, we determine the rank of γ tensored (over Z);with various fields. Our main result depends only on the functoriality of

Keywords

16A2620K0513F9918F99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986 , pp. 79 - 83
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Hasse, H., Vorlesungen iiber Klassenkürpertheorie, Physica-Verlag, Würzburg (1967).Google Scholar
2. Hoechsmann, K. Sehgal, S. K., Weiss, A., Cyclotomic Units and the Unit Group of an Elementary Abelian Group Ring, to appear.Google Scholar
3. Sehgal, S. K., Topics in Group Rings, Marcel Dekker, New York (1978).Google Scholar