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ON THE CONJUGACY PROBLEM IN CERTAIN METABELIAN GROUPS

Published online by Cambridge University Press:  20 June 2018

JONATHAN GRYAK ,
DELARAM KAHROBAEI  and
CONCHITA MARTINEZ-PEREZ
JONATHAN GRYAK
Affiliation:
Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI, USA e-mail: gryakj@med.umich.edu
DELARAM KAHROBAEI
Affiliation:
CUNY Graduate Center, PhD Program in Computer Science and NYCCT, Mathematics Department, City University of New York, New York, NY, USA e-mail: dkahrobaei@gc.cuny.edu
CONCHITA MARTINEZ-PEREZ
Affiliation:
Department of Mathematics, University of Zaragoza, Zaragoza, Spain e-mail: conmar@unizar.es
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Abstract

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We analyze the computational complexity of an algorithm to solve the conjugacy search problem in a certain family of metabelian groups. We prove that in general the time complexity of the conjugacy search problem for these groups is at most exponential. For a subfamily of groups, we prove that the conjugacy search problem is polynomial. We also show that for a different subfamily the conjugacy search problem reduces to the discrete logarithm problem.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 2 , May 2019 , pp. 251 - 269
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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