Geodesic
Conjugacy problem in an automorphism group of an infinite tree
Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 592-597.

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An algorithm recognizing the conjugacy of elements in the Grigorchuk 2-group is constructed. 
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     title = {Conjugacy problem in an automorphism group of an infinite tree},
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A. V. Rozhkov. Conjugacy problem in an automorphism group of an infinite tree. Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 592-597. http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a11/

[1] Grigorchuk R. I., “K probleme Bernsaida o periodicheskikh gruppakh”, Funktsion. analiz i ego prilozh., 14:1 (1980), 53–54 | MR | Zbl

[2] Rozhkov A. V., “Tsentralizatory elementov v odnoi gruppe avtomorfizmov derevev”, Izv. RAN. Ser. matem., 57:6 (1993), 82–105 | Zbl

[3] Wilson J. S., Zalesskii P. A., “Conjugacy separability of certain torsion groups”, Arch. Math. (Basel), 68 (1997), 441–449 | MR | Zbl