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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 470, Pages 38–49 (Mi znsl6610)  
This article is cited in 8 scientific papers (total in 8 papers)

Unrelativised standard commutator formula

N. Vavilov

St. Petersburg State University
Full-text PDF (171 kB) Citations (8)
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Abstract: In the present note, which is a marginalia to the previous papers by Roozbeh Hazrat, Alexei Stepanov, Zuhong Zhang, and the author, I observe that for any ideals $A,B\unlhd R$ of a commutative ring $R$ and all $n\ge3$ the birelative standard commutator formula also holds in the unrelativised form, as $[E(n,A),\mathrm{GL}(n,B)]=[E(n,A),E(n,B)]$ and discuss some obvious corollaries thereof.
Key words and phrases: general linear group, congruence subgroups, elementary subgroups, standard commutator formulae.
Funding agency Grant number
Russian Science Foundation 17-11-01261
This publication is supported by Russian Science Foundation grant 17-11-01261.
Received: 23.10.2018
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 243, Issue 4, Pages 527–534
DOI: https://doi.org/10.1007/s10958-019-04554-w
Bibliographic databases:
Document Type: Article
UDC: 512.5
Language: English
Citation: N. Vavilov, “Unrelativised standard commutator formula”, Problems in the theory of representations of algebras and groups. Part 33, Zap. Nauchn. Sem. POMI, 470, POMI, St. Petersburg, 2018, 38–49; J. Math. Sci. (N. Y.), 243:4 (2019), 527–534
Citation in format AMSBIB
\Bibitem{Vav18}
\by N.~Vavilov
\paper Unrelativised standard commutator formula
\inbook Problems in the theory of representations of algebras and groups. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 470
\pages 38--49
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6610}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 243
\issue 4
\pages 527--534
\crossref{https://doi.org/10.1007/s10958-019-04554-w}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074852524}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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