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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 2, Pages 109–128 (Mi izv14)  

This article is cited in 1 scientific paper (total in 1 paper)

On the decomposition of automorphisms of free modules into simple factors

V. G. Bardakov


Abstract: We study decompositions of automorphisms of various free modules into products of transvections and dilations. In particular, for a free $\mathbb Z$-module $M=\mathbb Z^n$ (where $n\geqslant 3$) we show that any automorphism $\sigma\in\operatorname{GL}_n(M)$ can be expressed as a product of not more than $2n+5$ transvections and one simple transformation which is a transvection if $\sigma\in\operatorname{SL}_n(M)$ and a dilation otherwise. As a corollary we obtain that for $n\geqslant 3$ the width of the group $\operatorname{SL}_n(\mathbb Z)$, with respect to the set of commutators, does not exceed 10.

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English version:
Izvestiya: Mathematics, 1995, 59:2, 333–351

Bibliographic databases:

MSC: 20F28
Received: 17.12.1992

Citation: V. G. Bardakov, “On the decomposition of automorphisms of free modules into simple factors”, Izv. RAN. Ser. Mat., 59:2 (1995), 109–128; Izv. Math., 59:2 (1995), 333–351

Citation in format AMSBIB
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\paper On the decomposition of automorphisms of free modules into simple factors
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 2
\pages 109--128
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\zmath{https://zbmath.org/?q=an:0896.20031}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 2
\pages 333--351
\crossref{https://doi.org/10.1070/IM1995v059n02ABEH000014}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RZ88800005}


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    This publication is cited in the following articles:
    1. N. A. Vavilov, A. V. Stepanov, “Linear groups over general rings. I. Generalities”, J. Math. Sci. (N. Y.), 188:5 (2013), 490–550  mathnet  crossref  mathscinet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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