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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 452, Pages 5–31 (Mi znsl6354)  
This article is cited in 3 scientific papers (total in 3 papers)

Local-global principle for general quadratic and general Hermitian groups and the nilpotence of $\mathrm{KH}_1$

R. Basu

Indian Institute of Science Education and Research — Pune, Maharashtra 411008, India
Full-text PDF (283 kB) Citations (3)
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Abstract: In this article we establish an analog of the Quillen–Suslin's local-global principle for the elementary subgroup of the general quadratic group and the general Hermitian group. We show that unstable $\mathrm K_1$-groups of general Hermitian groups over module finite rings are nilpotent-by-abelian. This generalizes earlier results of A. Bak, R. Hazrat, and N. Vavilov.
Key words and phrases: bilinear forms, quadratic forms.
Received: 11.10.2016
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 232, Issue 5, Pages 591–609
DOI: https://doi.org/10.1007/s10958-018-3891-0
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: English
Citation: R. Basu, “Local-global principle for general quadratic and general Hermitian groups and the nilpotence of $\mathrm{KH}_1$”, Problems in the theory of representations of algebras and groups. Part 30, Zap. Nauchn. Sem. POMI, 452, POMI, St. Petersburg, 2016, 5–31; J. Math. Sci. (N. Y.), 232:5 (2018), 591–609
Citation in format AMSBIB
\Bibitem{Bas16}
\by R.~Basu
\paper Local-global principle for general quadratic and general Hermitian groups and the nilpotence of~$\mathrm{KH}_1$
\inbook Problems in the theory of representations of algebras and groups. Part~30
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 452
\pages 5--31
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6354}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3589281}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 232
\issue 5
\pages 591--609
\crossref{https://doi.org/10.1007/s10958-018-3891-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048499482}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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