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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board Member: Blackburn, Simon R. / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Schäge, Sven / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

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Equations over groups

Vitaliĭ Roman'kov
  • Institute of Mathematics and Information Technologies, Omsk State Dostoevskii University, Russia
  • :
Published Online: 2012-11-27 | DOI: https://doi.org/10.1515/gcc-2012-0015


This paper is a survey of known results (old and new) about equations over groups, mainly solvable groups. Current directions of research are discussed in some detail. A number of open questions are included.

Keywords: Equation; solution; solvability; free groups; nilpotent groups; solvable groups; finite approximability; verbal width; word map; asymptotic density

Received: 2012-06-22

Published Online: 2012-11-27

Published in Print: 2012-12-01

Citation Information: . Volume 4, Issue 2, Pages 191–239, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2012-0015, November 2012

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