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Zapiski Nauchnykh Seminarov LOMI, 1978, Volume 75, Pages 22–31
(Mi znsl3782)
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This article is cited in 33 scientific papers (total in 33 papers)
Subgroups of linear groups rich in transvections
Z. I. Borevich
Abstract:
Let $K$ be a field and let $k$ be a subfield of it. Subgroups $H$ in $\mathrm{GL}(n,K)$ are considered which contain all diagonal matrices with nonzero elements in the subfield $k$. It is said that $H$ is rich in transvections if for any pair of indices $i\ne j$ $H$ contains a transvection with a nonzero element in the position $(i,j)$. In the work a description is given of all intermediate subgroups $H$ rich in transvections under the condition that $n\ge3$, $(K:k)\ge3$. A similar question is solved also for the special linear group. Bibl. 5 titles.
Citation:
Z. I. Borevich, “Subgroups of linear groups rich in transvections”, Rings and linear groups, Zap. Nauchn. Sem. LOMI, 75, "Nauka", Leningrad. Otdel., Leningrad, 1978, 22–31; J. Soviet Math., 37:2 (1987), 928–934
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https://www.mathnet.ru/eng/znsl3782 https://www.mathnet.ru/eng/znsl/v75/p22
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Abstract page: | 231 | Full-text PDF : | 76 |
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