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Algorithmic Aspects of Units in Group Rings

In: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory

Author

Listed:
  • Andreas Bächle

    (Vrije Universiteit Brussel, Vakgroep Wiskunde)

  • Wolfgang Kimmerle

    (Universität Stuttgart, Fachbereich Mathematik, IGT)

  • Leo Margolis

    (Universidad de Murcia, Departamento de matemáticas, Facultad de matemáticas)

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.

Suggested Citation

  • Andreas Bächle & Wolfgang Kimmerle & Leo Margolis, 2017. "Algorithmic Aspects of Units in Group Rings," Springer Books, in: Gebhard Böckle & Wolfram Decker & Gunter Malle (ed.), Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, pages 1-22, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-70566-8_1
    DOI: 10.1007/978-3-319-70566-8_1
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