Computing generators of the unit group of an integral abelian group ring

Paolo Faccin; Wilhelm Plesken; Willem A. de Graaf

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Computing generators of the unit group of an integral abelian group ring

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arxiv 1301.1770 v1 pith:JFUA4KR4 submitted 2013-01-09 math.RA

Computing generators of the unit group of an integral abelian group ring

Paolo Faccin , Willem A. de Graaf , Wilhelm Plesken This is my paper

classification math.RA

keywords groupunitalgorithmgeneratorsabeliandescribeintegralring

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We describe an algorithm for obtaining generators of the unit group of the integral group ring ZG of a finite abelian group G. We used our implementation in Magma of this algorithm to compute the unit groups of ZG for G of order up to 110. In particular for those cases we obtained the index of the group of Hoechsmann units in the full unit group. At the end of the paper we describe an algorithm for the more general problem of finding generators of an arithmetic group corresponding to a diagonalizable algebraic group.

Computing generators of the unit group of an integral abelian group ring

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