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Zassenhaus Conjecture (ZC1) on torsion units of integral group rings for some metabelian groups

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Abstract.

We prove a conjecture of Zassenhaus that every normalized torsion unit of the integral group ring ZG of a finite group G is rationally conjugate to a group element for some metabelian groups including metacyclic groups G containing a normal cyclic group A such that G/A is cyclic of prime power order. The relative prime case was done in [11].

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Authors and Affiliations

  1. Dep. de Matemáticas, Universidad de Murcia, E-30100, Murcia, Spain

    Ángel del Río

  2. Dep. of Math. and Stat. Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

    Sudarshan K. Sehgal

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  1. Ángel del Río
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  2. Sudarshan K. Sehgal
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Correspondence to Ángel del Río.

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Received: 21 April 2005

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Río, Á.d., Sehgal, S.K. Zassenhaus Conjecture (ZC1) on torsion units of integral group rings for some metabelian groups. Arch. Math. 86, 392–397 (2006). https://doi.org/10.1007/s00013-005-1554-0

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  • DOI: https://doi.org/10.1007/s00013-005-1554-0

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