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Zap. Nauchn. Sem. POMI, 2015, Volume 435, Pages 33–41 (Mi znsl6149)  

This article is cited in 4 scientific papers (total in 4 papers)

Decomposition of elementary transvection in elementary group

R. Yu. Dryaevaa, V. A. Koibaevab

a North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz, Russia
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia

Abstract: We consider the following data: an elementary net (or, what is the same elementary carpet) $\sigma=\sigma_{ij})$ of additive subgroups of a commutative ring (in other words, a net without the diagonal) of order $n$, a derived net $\omega=(\omega_{ij})$, which depends of the net $\sigma$, the net $\Omega=(\Omega_{ij})$, associated with the elementary group $E(\sigma)$, where $\omega\subseteq\sigma\subseteq\Omega$ and the net $\Omega$ is the smallest (complemented) net among the all nets which contain the elementary net $\sigma$. We prove that every elementary transvection $t_{ij}(\alpha)$ can be decomposed as a product of two matrices $M_1$ and $M_2$, where $M_1$ belongs to the group $\langle t_{ij}\sigma_{ij}),t_{ji}(\sigma_{ji})\rangle$, $M_2$ belongs to the net group $G(\tau)$ and the net $\tau$ has the form $\tau=\begin{pmatrix}\Omega_{11}&\omega_{12}
\omega_{21}&\Omega_{22}\end{pmatrix}$.

Key words and phrases: nets, elementary nets, closed nets, net groups, elementary group, transvection.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00469


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English version:
Journal of Mathematical Sciences (New York), 2016, 219:4, 513–518

Bibliographic databases:

UDC: 512.5
Received: 23.09.2015

Citation: R. Yu. Dryaeva, V. A. Koibaev, “Decomposition of elementary transvection in elementary group”, Problems in the theory of representations of algebras and groups. Part 28, Zap. Nauchn. Sem. POMI, 435, POMI, St. Petersburg, 2015, 33–41; J. Math. Sci. (N. Y.), 219:4 (2016), 513–518

Citation in format AMSBIB
\Bibitem{DryKoi15}
\by R.~Yu.~Dryaeva, V.~A.~Koibaev
\paper Decomposition of elementary transvection in elementary group
\inbook Problems in the theory of representations of algebras and groups. Part~28
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 435
\pages 33--41
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6149}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3493615}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 219
\issue 4
\pages 513--518
\crossref{https://doi.org/10.1007/s10958-016-3123-4}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. A. Dzhusoeva, R. Yu. Dryaeva, “Tsiklicheskie elementarnye seti”, Vladikavk. matem. zhurn., 19:1 (2017), 26–29  mathnet
    2. Vladimir A. Koibaev, “On a question about generalized congruence subgroups”, Zhurn. SFU. Ser. Matem. i fiz., 11:1 (2018), 66–69  mathnet  crossref
    3. V. A. Koibaev, “On a question about generalized congruence subgroups. I”, J. Math. Sci. (N. Y.), 243:4 (2019), 573–576  mathnet  crossref
    4. S. Yu. Itarova, V. A. Koibaev, “Razlozhenie elementarnoi transvektsii v elementarnoi setevoi gruppe”, Vladikavk. matem. zhurn., 21:3 (2019), 24–30  mathnet  crossref
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