Hurwitz equivalence in tuples of dihedral groups, dicyclic groups, and semidihedral groups.

Charmaine Sia

The electronic journal of combinatorics, Tome 16 (2009) no. 1

Résumé

Let $D_{2N}$ be the dihedral group of order $2N$, ${\it Dic}_{4M}$ 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 $D_{2N}^n$, ${\it Dic}_{4M}^n$, $SD_{2^m}^n$, and $M_{2^m}^n$ under the Hurwitz action.

Détail

DOI : 10.37236/184

Classification : 20F36, 20C15, 20F05
Mots-clés : dihedral groups, dicyclic groups, semidihedral groups, orbits, Hurwitz actions, actions of braid groups