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RESEARCH PRODUCT

MR 2776821 Reviewed Berger E. Hurwitz equivalence in dihedral groups. The Electronic Journal of Combinatorics 18 (2011), no.1, paper 45, 16 pp. (Reviewer Francesca Vetro) 20F36

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In the paper under review, the author studies the orbits of the action of the braid group B_{n} on G^{n} where G denoted a dihedral group. At first, the author considers tuples T consisting only of reflections. In this case, the author proves that the orbits are determinate by three invariants. These invariants are the product of the entries, the subgroup generated by the entries and the number of times each conjugacy class is represented in T. Successively, the author works with tuples whose entries are any elements of dihedral groups. The author shows that, also this time, the above invariants are sufficient in order to determinate the orbits of the action of B_{n} on G^{n}.