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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura / Lohrey, Markus

CiteScore 2018: 0.80

SCImago Journal Rank (SJR) 2018: 0.368
Source Normalized Impact per Paper (SNIP) 2018: 1.061

Mathematical Citation Quotient (MCQ) 2017: 0.32

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Group-theoretic orbit decidability

Enric Ventura
  • Departament de Matemàtica Aplicada III, Escola Politècnica Superior d'Enginyeria de Manresa, Universitat Politècnica de Catalunya, Av. Bases de Manresa 61-73 08242-Manresa, Barcelona (Catalonia), Spain
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Published Online: 2014-10-23 | DOI: https://doi.org/10.1515/gcc-2014-0012


A recent collection of papers in the last years have given a renovated interest to the notion of orbit decidability. This is a new quite general algorithmic notion, connecting with several classical results, and closely related to the study of the conjugacy problem for extensions of groups. In the present survey we explain several of the classical results closely related to this concept, and we explain the main ideas behind the recent connection with the conjugacy problem made by Bogopolski–Martino–Ventura in [Trans. Amer. Math. Soc. 362 (2010), 2003–2036]. All the consequences up to date, published in several other papers by other authors, are also commented and reviewed.

Keywords: Orbit decidability; conjugacy problem

MSC: 20F10; 20F28

About the article

Received: 2014-09-17

Published Online: 2014-10-23

Published in Print: 2014-11-01

Funding Source: Spanish Government

Award identifier / Grant number: MTM2011-25955

Citation Information: Groups Complexity Cryptology, Volume 6, Issue 2, Pages 133–148, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2014-0012.

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