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(S2) if and only if n is even. If n is divisible by 4 then the commutator subgroup of B\n(S2) contains such a subgroup. Further, for all n greater than or equal to 3, B\n(S2) contains a subgroup isomorphic to the dicyclic group of order 4n.
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