Subgroups of the full linear group over a semilocal ring

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Subgroups of the full linear group over a semilocal ring. / Borevich, Z. I.; Vavilov, N. A.

In: Journal of Soviet Mathematics, Vol. 37, No. 2, 04.1987, p. 935-937.

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Borevich, Z. I. ; Vavilov, N. A. / Subgroups of the full linear group over a semilocal ring. In: Journal of Soviet Mathematics. 1987 ; Vol. 37, No. 2. pp. 935-937.

BibTeX

@article{d86a72465f874aa0911c939d5ee1e53f,

title = "Subgroups of the full linear group over a semilocal ring",

abstract = "Let Λ 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⊂C contains no fewer than seven elements. The structure of subgroups H in the full linear group GL(n, Λ) containing the group of diagonal matrices is considered. The main theorem: for any subgroup H there is a uniquely determined D-net of ideals σ such that G(σ)≤H≤N(σ), where N(σ) is the normalizer of the D-net subgroup σ. A transparent classification of subgroups GL(n, Λ) normalizable by diagonal matrices is thus obtained. Further, the factor group N(σ)/G(σ) is studied.",

author = "Borevich, {Z. I.} and Vavilov, {N. A.}",

year = "1987",

month = apr,

doi = "10.1007/BF01089084",

language = "English",

volume = "37",

pages = "935--937",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "2",

}

RIS

TY - JOUR

T1 - Subgroups of the full linear group over a semilocal ring

AU - Borevich, Z. I.

AU - Vavilov, N. A.

PY - 1987/4

Y1 - 1987/4

N2 - Let Λ 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⊂C contains no fewer than seven elements. The structure of subgroups H in the full linear group GL(n, Λ) containing the group of diagonal matrices is considered. The main theorem: for any subgroup H there is a uniquely determined D-net of ideals σ such that G(σ)≤H≤N(σ), where N(σ) is the normalizer of the D-net subgroup σ. A transparent classification of subgroups GL(n, Λ) normalizable by diagonal matrices is thus obtained. Further, the factor group N(σ)/G(σ) is studied.

AB - Let Λ 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⊂C contains no fewer than seven elements. The structure of subgroups H in the full linear group GL(n, Λ) containing the group of diagonal matrices is considered. The main theorem: for any subgroup H there is a uniquely determined D-net of ideals σ such that G(σ)≤H≤N(σ), where N(σ) is the normalizer of the D-net subgroup σ. A transparent classification of subgroups GL(n, Λ) normalizable by diagonal matrices is thus obtained. Further, the factor group N(σ)/G(σ) is studied.

UR - http://www.scopus.com/inward/record.url?scp=34250106432&partnerID=8YFLogxK

U2 - 10.1007/BF01089084

DO - 10.1007/BF01089084

M3 - Article

AN - SCOPUS:34250106432

VL - 37

SP - 935

EP - 937

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 2

ER -

ID: 76484977