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The ranks of central unit groups of integral group rings of alternating groups

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Let G be a finite group and U(Z(Z G)) be the group of units of the center Z(Z G) of the integral group ring Z G (the central unit group of the ring Z G). The purpose of the present work is to study the ranks r n of groups U(Z(ZAn)), i.e., of central unit groups of integral group rings of alternating groups A n . We shall find all values n for r n = 1 and propose an approach on how to describe the groups U(Z(ZAn)) in these cases, and we will present some results of calculations of r n for n ≤ 600.

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Authors and Affiliations

  1. Faculty of Mathematics and Mechanics, South Ural State University, Lenin av., 80, 454080, Chelyabinsk, Russia

    R. Zh. Aleev, A. V. Kargapolov & V. V. Sokolov

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  1. R. Zh. Aleev
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  2. A. V. Kargapolov
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  3. V. V. Sokolov
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Correspondence to R. Zh. Aleev.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 14, No. 7, pp. 15–21, 2008.

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Aleev, R.Z., Kargapolov, A.V. & Sokolov, V.V. The ranks of central unit groups of integral group rings of alternating groups. J Math Sci 164, 163–167 (2010). https://doi.org/10.1007/s10958-009-9746-y

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  • DOI: https://doi.org/10.1007/s10958-009-9746-y

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