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On central unit groups of integral group rings of alternating groups

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Abstract

The basic aim of this paper is to give a full description of central unit groups of integral group rings of alternating groups in the case when the central unit group has rank 1. The results are obtained in two steps. First, it is proved that the generator of the central unit group is local. Then, its exact value is found.

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References

  1. R. Zh. Aleev, Mat. Tr. 3(1), 3 (2000); English transl.: Siberian Adv. Math. 11 (1), 1 (2001).

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  2. R. A. Ferraz, J. Algebra 279(1), 191 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  3. R. Zh. Aleev and V. V. Sokolov, in Abstr. VII Intern. Conf. “Group Theory” (Chelyabinsk, 2008), pp. 14–15 [in Russian].

  4. GAP: A System for Computational Discrete Algebra, http://www.gap-system.org.

  5. Z. I. Borevich and I. R. Shafarevich, Number Theory (Nauka, Moscow, 1964; Academic, New York, 1966).

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  6. R. Zh. Aleev, Mat. Tr. 3(2), 3 (2000); English transl.: Siberian Adv. Math. 11 (2), 1 (2001).

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Authors and Affiliations

  1. South Ural State University, pr. Lenina 76, Chelyabinsk, 454080, Russia

    R. Zh. Aleev & V. V. Sokolov

Authors
  1. R. Zh. Aleev
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  2. V. V. Sokolov
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Correspondence to R. Zh. Aleev.

Additional information

Original Russian Text © R.Zh. Aleev, V.V. Sokolov, 2009, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Vol. 15, No. 2.

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Aleev, R.Z., Sokolov, V.V. On central unit groups of integral group rings of alternating groups. Proc. Steklov Inst. Math. 267 (Suppl 1), 1–9 (2009). https://doi.org/10.1134/S0081543809070013

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  • DOI: https://doi.org/10.1134/S0081543809070013

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