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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus


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5-year IMPACT FACTOR: 0.520

CiteScore 2018: 0.53

SCImago Journal Rank (SJR) 2018: 0.566
Source Normalized Impact per Paper (SNIP) 2018: 1.047

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1435-4446
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Volume 10, Issue 4

Issues

An algorithm that decides translation equivalence in a free group of rank two

Donghi Lee
Published Online: 2007-07-26 | DOI: https://doi.org/10.1515/JGT.2007.043

Abstract

Let F 2 be a free group of rank 2. We prove that there is an algorithm that decides whether or not, for two given elements u, v of F 2, u and v are translation equivalent in F 2, that is, whether or not u and v have the property that the cyclic length of (u) equals the cyclic length of (v) for every automorphism of F 2. This gives an affirmative solution to problem F38a in the online version (http://www.grouptheory.info) of [G. Baumslag, A. G. Myasnikov and V. Shpilrain. Open problems in combinatorial group theory, 2nd edn. In Combinatorial and geometric group theory (New York, 2000/Hoboken, NJ, 2001), Contemp. Math. 296 (American Mathematical Society, 2002), pp. 1–38.] for the case of F 2.

About the article


Received: 2006-03-17

Published Online: 2007-07-26

Published in Print: 2007-07-20


Citation Information: Journal of Group Theory, Volume 10, Issue 4, Pages 561–569, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/JGT.2007.043.

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[1]
Donghi Lee
Journal of Algebra, 2009, Volume 321, Number 1, Page 167
[2]
Donghi Lee and Enric Ventura
Journal of Algebra, 2010, Volume 324, Number 2, Page 195

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