Geodesic
ON THE CONJUGACY PROBLEM IN CERTAIN METABELIAN GROUPS
Glasgow mathematical journal, Tome 61 (2019) no. 2, pp. 251-269

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DOI

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. 
GRYAK, JONATHAN; KAHROBAEI, DELARAM; MARTINEZ-PEREZ, CONCHITA. ON THE CONJUGACY PROBLEM IN CERTAIN METABELIAN GROUPS. Glasgow mathematical journal, Tome 61 (2019) no. 2, pp. 251-269. doi: 10.1017/S0017089518000198
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     title = {ON {THE} {CONJUGACY} {PROBLEM} {IN} {CERTAIN} {METABELIAN} {GROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {251--269},
     year = {2019},
     volume = {61},
     number = {2},
     doi = {10.1017/S0017089518000198},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000198/}
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