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Hurwitz equivalence in tuples of dihedral groups, dicyclic groups, and semidihedral groups. (English) Zbl 1191.20035
Summary: Let $$D_{2N}$$ be the dihedral group of order $$2N$$, $$\text{Dic}_{4M}$$ the dicyclic group of order $$4M$$, $$SD_{2^m}$$ the semidihedral group of order $$2^m$$, and $$M_{2^m}$$ the group of order $$2^m$$ with presentation $$M_{2^m}=\langle\alpha,\beta\mid\alpha^{2^{m-1}}=\beta^2=1$$, $$\beta\alpha\beta^{-1}=\alpha^{2^{m-2}+1}\rangle$$. We classify the orbits in $$D_{2N}^n$$, $$\text{Dic}_{4M}^n$$, $$SD_{2^m}^n$$, and $$M_{2^m}^n$$ under the Hurwitz action.

##### MSC:
 20F36 Braid groups; Artin groups 20C15 Ordinary representations and characters 20F05 Generators, relations, and presentations of groups
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