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Transactions of the American Mathematical Society

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Magnus embedding and algorithmic properties of groups $ F/N^{(d)}$


Authors: Funda Gul, Mahmood Sohrabi and Alexander Ushakov
Journal: Trans. Amer. Math. Soc. 369 (2017), 6189-6206
MSC (2010): Primary 20F19, 20F10, 20F65, 03D15
DOI: https://doi.org/10.1090/tran/6880
Published electronically: November 28, 2016
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Abstract: In this paper we further study properties of Magnus embedding, give a precise reducibility diagram for Dehn problems in groups of the form $ F/N^{(d)}$, and provide a detailed answer to Problem 12.98 in The Kourovka notebook. We also show that most of the reductions are polynomial time reductions and can be used in practical computation.


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Additional Information

Funda Gul
Affiliation: Department of Mathematics, Stevens Institute of Technology, Hoboken, New Jersey 07030
Email: fgul@stevens.edu

Mahmood Sohrabi
Affiliation: Department of Mathematics, Stevens Institute of Technology, Hoboken, New Jersey 07030
Email: msohrab1@stevens.edu

Alexander Ushakov
Affiliation: Department of Mathematics, Stevens Institute of Technology, Hoboken, New Jersey 07030
Email: aushakov@stevens.edu

DOI: https://doi.org/10.1090/tran/6880
Keywords: Magnus embedding, word problem, power problem, conjugacy problem, free solvable groups
Received by editor(s): March 11, 2015
Received by editor(s) in revised form: September 15, 2015
Published electronically: November 28, 2016
Additional Notes: The third author was partially supported by NSA Mathematical Sciences Program grant number H98230-14-1-0128
Article copyright: © Copyright 2016 American Mathematical Society

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