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Zapiski Nauchnykh Seminarov LOMI, 1978, Volume 75, Pages 32–34
(Mi znsl3783)
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Subgroups of the full linear group over a semilocal ring
Z. I. Borevich, N. A. Vavilov
Abstract:
Let $\Lambda$ be a semilocal ring (a factor ring with respect to the Jacobson–Artin radical) for which the residue field $C/m$ of its center $C$ with respect to each maximal ideal $m\subset C$ contains no fewer than seven elements. The structure of subgroups $H$ in the full linear group $\mathrm{GL}(n,\Lambda)$ containing the group of diagonal matrices is considered. The main theorem: for any subgroup $H$ there is a uniquely determined $D$-net of ideals $\sigma$ such that $G(\sigma)\le H\le N(\sigma)$, where $N(\sigma)$ is the normalizer of the $D$-net subgroup $G(\sigma)$. A transparent classification of subgroups $\mathrm{GL}(n,\Lambda)$ normalizable by diagonal matrices is thus obtained. Further, the factor group $N(\sigma)/G(\sigma)$ is studied. Bibl. 4 titles.
Citation:
Z. I. Borevich, N. A. Vavilov, “Subgroups of the full linear group over a semilocal ring”, Rings and linear groups, Zap. Nauchn. Sem. LOMI, 75, "Nauka", Leningrad. Otdel., Leningrad, 1978, 32–34; J. Soviet Math., 37:2 (1987), 935–937
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https://www.mathnet.ru/eng/znsl3783 https://www.mathnet.ru/eng/znsl/v75/p32
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Abstract page: | 195 | Full-text PDF : | 83 |
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