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Matematicheskie Zametki, 1995, Volume 58, Issue 4, Pages 569–581 (Mi mzm2077)  
Parametric equations in free groups

Yu. I. Ozhigov

Moscow State Technological University "Stankin"
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Abstract: We introduce the notion of a parametric equation in a free group; this is an equation containing natural parameters as exponents and a system of linear Diophantine equations relating these exponents. For these equations, we introduce elementary transformations that are necessary for the description of general solutions of ordinary equations in a free group. We prove that it is possible to linearize any relation among parameters that appears in the course of transformations of the given equation.
Received: 04.01.1994
English version:
Mathematical Notes, 1995, Volume 58, Issue 4, Pages 1074–1083
DOI: https://doi.org/10.1007/BF02305096
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Language: Russian
Citation: Yu. I. Ozhigov, “Parametric equations in free groups”, Mat. Zametki, 58:4 (1995), 569–581; Math. Notes, 58:4 (1995), 1074–1083
Citation in format AMSBIB
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\by Yu.~I.~Ozhigov
\paper Parametric equations in free groups
\jour Mat. Zametki
\yr 1995
\vol 58
\issue 4
\pages 569--581
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1378337}
\zmath{https://zbmath.org/?q=an:0855.20025}
\transl
\jour Math. Notes
\yr 1995
\vol 58
\issue 4
\pages 1074--1083
\crossref{https://doi.org/10.1007/BF02305096}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TW84800029}
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