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Fundamentalnaya i Prikladnaya Matematika, 2008, Volume 14, Issue 7, Pages 15–21
(Mi fpm1169)
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This article is cited in 5 scientific papers (total in 5 papers)
The ranks of central unit groups of integral group rings of alternating groups
R. Zh. Aleev, A. V. Kargapolov, V. V. Sokolov Southern Ural State University
Abstract:
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 $n\leq600$.
Citation:
R. Zh. Aleev, A. V. Kargapolov, V. V. Sokolov, “The ranks of central unit groups of integral group rings of alternating groups”, Fundam. Prikl. Mat., 14:7 (2008), 15–21; J. Math. Sci., 164:2 (2010), 163–167
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https://www.mathnet.ru/eng/fpm1169 https://www.mathnet.ru/eng/fpm/v14/i7/p15
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Abstract page: | 412 | Full-text PDF : | 162 | References: | 56 | First page: | 1 |
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