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Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory pp 1–22Cite as

Algorithmic Aspects of Units in Group Rings

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Abstract

We describe the main questions connected to torsion subgroups in the unit group of integral group rings of finite groups and algorithmic methods to attack these questions. We then prove the Zassenhaus Conjecture for Amitsur groups and prove that any normalized torsion subgroup in the unit group of an integral group of a Frobenius complement is isomorphic to a subgroup of the group base. Moreover we study the orders of torsion units in integral group rings of finite almost quasisimple groups and the existence of torsion-free normal subgroups of finite index in the unit group.

The first author is a postdoctoral researcher of the FWO (Research Foundation Flanders). The third is supported by a Marie Skłodowska-Curie Individual Fellowship from EU project 705112-ZC.

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Author information

Authors and Affiliations

  1. Vakgroep Wiskunde, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium

    Andreas Bächle

  2. Fachbereich Mathematik, IGT, Universität Stuttgart, Pfaffenwaldring 57, 70550, Stuttgart, Germany

    Wolfgang Kimmerle

  3. Departamento de matemáticas, Facultad de matemáticas, Universidad de Murcia, 30100, Murcia, Spain

    Leo Margolis

Authors
  1. Andreas Bächle
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  2. Wolfgang Kimmerle
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  3. Leo Margolis
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Correspondence to Wolfgang Kimmerle .

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Editors and Affiliations

  1. IWR, Heidelberg University, Heidelberg, Germany

    Gebhard Böckle

  2. Department of Mathematics, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Wolfram Decker

  3. Department of Mathematics, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Gunter Malle

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Bächle, A., Kimmerle, W., Margolis, L. (2017). Algorithmic Aspects of Units in Group Rings. In: Böckle, G., Decker, W., Malle, G. (eds) Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-70566-8_1

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