Subgroups of the General Linear Group That Contain Elementary Subgroup Over a Rank 2 Commutative Ring Extension

Let R = ∏ i ∈ I F i be the direct product of fields, and let S = R d = ∏ i ∈ I F i d i be a rank 2 extension of R. The subgroups of the general linear group GL(2n,R), n ≥ 3, that contain the elementary group E (n, S) are described. It is shown that for every such a subgroup H there exists a unique i...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 234; no. 2; pp. 256 - 267
Main Authors Hoi, T. N., Nhat, N. H. T.
Format Journal Article
LanguageEnglish
Published New York Springer US 02.10.2018
Springer
Springer Nature B.V
Subjects
Commutativity
Mathematics
Mathematics and Statistics
Rings (mathematics)
Subgroups
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Summary:Let R = ∏ i ∈ I F i be the direct product of fields, and let S = R d = ∏ i ∈ I F i d i be a rank 2 extension of R. The subgroups of the general linear group GL(2n,R), n ≥ 3, that contain the elementary group E (n, S) are described. It is shown that for every such a subgroup H there exists a unique ideal A ⊴ R such that E (n, S)E(2n,R,A) ≤ H ≤ N GL(2n,R) (E (n, S)E(2n,R,A)).
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-018-4001-z