The quaternion group as a subgroup of the sphere braid groups

Details The quaternion group as a subgroup of the sphere braid groups The quaternion group as a subgroup of the sphere braid groups

2006-03-15

arxiv.org/abs/math/0603377v1

Bulletin of the London Mathematical Society / The Bulletin of the London Mathematical Society 39, 2 (01/04/2007) 232-234

Mathematics

Geometric Topology

3 pages

Scientific paper

10.1112/blms/bdl041

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.

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