Geodesic
Hurwitz equivalence in dihedral groups.
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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In this paper we determine the orbits of the braid group $B_n$ action on $G^n$ when $G$ is a dihedral group and for any $T \in G^n$. We prove that the following invariants serve as necessary and sufficient conditions for Hurwitz equivalence. They are: the product of its entries, the subgroup generated by its entries, and the number of times each conjugacy class (in the subgroup generated by its entries) is represented in $T$.
DOI : 10.37236/532
Classification : 20F36, 20C15, 20F55
Mots-clés : dihedral groups, orbits, Hurwitz actions, actions of braid groups 
@article{10_37236_532,
     author = {Emily Berger},
     title = {Hurwitz equivalence in dihedral groups.},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/532},
     zbl = {1217.20023},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/532/}
}
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Emily Berger. Hurwitz equivalence in dihedral groups.. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/532

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