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The ranks of central unit groups of integral group rings of alternating groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 15-21
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Let $G$ be a finite group and $\mathrm U(Z(\mathbf ZG))$ be the group of units of the center $Z(\mathbf ZG)$ of the integral group ring $\mathbf ZG$ (the central unit group of the ring $\mathbf ZG$). The purpose of the present work is to study the ranks $r_n$ of groups $\mathrm U(Z(\mathbf Z\mathrm A_n)$, i.e., of central unit groups of integral group rings of alternating groups $\mathrm A_n$. We shall find all values $n$ for $r_n=1$ and propose an approach how to describe the groups $\mathrm U(Z(\mathbf Z\mathrm A_n))$ in these cases, and we will present some results of calculations of $r_n$ for $n\leq600$. 
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     title = {The ranks of central unit groups of integral group rings of alternating groups},
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R. Zh. Aleev; A. V. Kargapolov; V. V. Sokolov. The ranks of central unit groups of integral group rings of alternating groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 15-21. http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a1/

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