Geodesic
Decision of the generalized conjugacy problem in Artin groups of large type
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 1, pp. 1-38
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In this paper we have proved that an Artin group of large type has solvable generalized conjugacy problem, centralizer of finitely generated subgroup is itself finitely generated and there is algorithm which gives its generators. 
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     author = {V. N. Bezverkhnii},
     title = {Decision of the~generalized conjugacy problem in {Artin} groups of large type},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1--38},
     year = {1999},
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V. N. Bezverkhnii. Decision of the generalized conjugacy problem in Artin groups of large type. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 1, pp. 1-38. http://geodesic.mathdoc.fr/item/FPM_1999_5_1_a0/