Zap. Nauchn. Sem. LOMI, 1979, Volume 86, Pages 30–33
This article is cited in 2 scientific papers (total in 2 papers)
Description of subgroups of the full linear group over a semilocal ring that contain the group of diagonal matrices
N. A. Vavilov
It has been proved (Ref. Zh. Mat., 1978, 9A237) that for a semilocal ring $\Lambda$ in which each residue field of the center contains at least seven elements we have the following description of subgroups of the full linear group $GL(n,\Lambda)$ that contain the group of diagonal matrices: for each such subgroup $H$ there is a uniquely defined $D$-net of ideals $\sigma$ (Ref. Zh. Mat., 1977, 2A288) such that $G(\sigma)\leqslant h\leqslant N(\sigma)$, ,where $N(\sigma)$ is the normalizer of the $\sigma$-net subgroup $G(\sigma)$. It is noted that this result is also true under the following weaker assumption: a decomposition of a quotient ring of the ring $\Lambda$ into a direct sum of full matrix rings over skew fields does not contain skew fields with centers of less than seven elements or the ring of second-order matrices over the field of two elements.
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Journal of Soviet Mathematics, 1981, 17:4, 1960–1963
N. A. Vavilov, “Description of subgroups of the full linear group over a semilocal ring that contain the group of diagonal matrices”, Algebraic numbers and finite groups, Zap. Nauchn. Sem. LOMI, 86, "Nauka", Leningrad. Otdel., Leningrad, 1979, 30–33; J. Soviet Math., 17:4 (1981), 1960–1963
Citation in format AMSBIB
\paper Description of subgroups of the full linear group over a semilocal ring that contain the group of diagonal matrices
\inbook Algebraic numbers and finite groups
\serial Zap. Nauchn. Sem. LOMI
\publ "Nauka", Leningrad. Otdel.
\jour J. Soviet Math.
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