Description of subgroups of the full linear group over a semilocal ring that contain the group of diagonal matrices

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Description of subgroups of the full linear group over a semilocal ring that contain the group of diagonal matrices. / Vavilov, N. A.

в: Journal of Soviet Mathematics, Том 17, № 4, 11.1981, стр. 1960-1963.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{8e4b692b05864013afb8007144d88588,

title = "Description of subgroups of the full linear group over a semilocal ring that contain the group of diagonal matrices",

abstract = "It has been proved (Ref. Zh. Mat., 1978, 9A237) that for a semilocal ring Λ 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,Λ) that contain the group of diagonal matrices: for each such subgroup H there is a uniquely defined D -net of ideals S (Ref. Zh. Mat., 1977, 2A288) such that G(S)≤H≤N(S),,where N(S) is the normalizer of the S -net subgroup G(S). It is noted that this result is also true under the following weaker assumption: a decomposition of a quotient ring of the ring Λ 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.",

author = "Vavilov, {N. A.}",

year = "1981",

month = nov,

doi = "10.1007/BF01465452",

language = "English",

volume = "17",

pages = "1960--1963",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "4",

}

RIS

TY - JOUR

T1 - Description of subgroups of the full linear group over a semilocal ring that contain the group of diagonal matrices

AU - Vavilov, N. A.

PY - 1981/11

Y1 - 1981/11

N2 - It has been proved (Ref. Zh. Mat., 1978, 9A237) that for a semilocal ring Λ 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,Λ) that contain the group of diagonal matrices: for each such subgroup H there is a uniquely defined D -net of ideals S (Ref. Zh. Mat., 1977, 2A288) such that G(S)≤H≤N(S),,where N(S) is the normalizer of the S -net subgroup G(S). It is noted that this result is also true under the following weaker assumption: a decomposition of a quotient ring of the ring Λ 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.

AB - It has been proved (Ref. Zh. Mat., 1978, 9A237) that for a semilocal ring Λ 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,Λ) that contain the group of diagonal matrices: for each such subgroup H there is a uniquely defined D -net of ideals S (Ref. Zh. Mat., 1977, 2A288) such that G(S)≤H≤N(S),,where N(S) is the normalizer of the S -net subgroup G(S). It is noted that this result is also true under the following weaker assumption: a decomposition of a quotient ring of the ring Λ 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.

UR - http://www.scopus.com/inward/record.url?scp=0345992786&partnerID=8YFLogxK

U2 - 10.1007/BF01465452

DO - 10.1007/BF01465452

M3 - Article

AN - SCOPUS:0345992786

VL - 17

SP - 1960

EP - 1963

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -

ID: 76482517