Geodesic
A solution of the power conjugacy problem for words in the Coxeter groups of extra large type
Diskretnaya Matematika, Tome 20 (2008) no. 3, pp. 101-110

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For Coxeter groups of extra large type, the power conjugacy problem for words and the problem of intersection of cyclic groups are solved; for the second problem we suggest an algorithm which for two elements finds the generator of the intersection of their cyclic subgroups. 
@article{DM_2008_20_3_a9,
     author = {V. N. Bezverkhnii and I. V. Dobrynina},
     title = {A solution of the power conjugacy problem for words in the {Coxeter} groups of extra large type},
     journal = {Diskretnaya Matematika},
     pages = {101--110},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2008_20_3_a9/}
}
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V. N. Bezverkhnii; I. V. Dobrynina. A solution of the power conjugacy problem for words in the Coxeter groups of extra large type. Diskretnaya Matematika, Tome 20 (2008) no. 3, pp. 101-110. http://geodesic.mathdoc.fr/item/DM_2008_20_3_a9/