Let G be an abelian group of order n and let U(ZG) denote the unit group of ZG, the group ring of G over the integers. In this paper we show how to compute quickly a bound on the index of U(ZG) in the unit group U(Gamma) of the product Gamma of certain cyclotomic rings, whose structure is very well known, in which ZG is naturally embedded.
On the index of the group of units of the integral group ring of finite abelian groups.
ACCIARO, Vincenzo
2015-01-01
Abstract
Let G be an abelian group of order n and let U(ZG) denote the unit group of ZG, the group ring of G over the integers. In this paper we show how to compute quickly a bound on the index of U(ZG) in the unit group U(Gamma) of the product Gamma of certain cyclotomic rings, whose structure is very well known, in which ZG is naturally embedded.File in questo prodotto:
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