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 diagonalisable algebraic group. © 2012 Elsevier Inc. All rights reserved.
Computing generators of the unit group of an integral abelian group ring / Faccin, Paolo; De Graaf, Willem Adriaan; W., Plesken. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 373:(2013), pp. 441-452. [10.1016/j.jalgebra.2012.09.031]
Computing generators of the unit group of an integral abelian group ring
Faccin, Paolo;De Graaf, Willem Adriaan;
2013-01-01
Abstract
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 diagonalisable algebraic group. © 2012 Elsevier Inc. All rights reserved.| File | Dimensione | Formato | |
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