×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: EMIS EuDML