Geodesic
Conjugacy problem in a class of 2-groups
Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 573-583

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In the paper, the conjugacy problem for elements of Grigorchuk 2-groups is solved. Each group is regarded from the viewpoint of rearrangement-like transformations of the interval $(0,1)$ and from the viewpoint of wreath products of groups. Several approaches are indicated that allow one to establish conjugacy conditions of elements. 
@article{MZM_1998_64_4_a9,
     author = {Yu. G. Leonov},
     title = {Conjugacy problem in a class of 2-groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {573--583},
     publisher = {mathdoc},
     volume = {64},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a9/}
}
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Yu. G. Leonov. Conjugacy problem in a class of 2-groups. Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 573-583. http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a9/