The quaternion group as a subgroup of the sphere braid groups

Abstract

Let n be greater than or equal to 3. We prove that the quaternion group of order 8 is realised as a subgroup of the sphere braid group B\_n(S^2) if and only if n is even. If n is divisible by 4 then the commutator subgroup of B\_n(S^2) contains such a subgroup. Further, for all n greater than or equal to 3, B\_n(S^2) contains a subgroup isomorphic to the dicyclic group of order 4n.

3 pages

References in corpus (1)

• The braid groups of the projective plane

Cited by in corpus (4)

• The classification and the conjugacy classes of the finite subgroups of the sphere braid groups
• Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane
• The braid groups of the projective plane and the Fadell-Neuwirth short exact sequence
• Lower central series, surface braid groups, surjections and permutations