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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*
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

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1986

References

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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