The quaternion group as a subgroup of the sphere braid groups

Daciberg Lima Gonçalves; John Guaschi

doi:10.1112/blms/bdl041

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The quaternion group as a subgroup of the sphere braid groups

Daciberg Lima Gonçalves·John Guaschi

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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.

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BibTeX RIS

Daciberg Lima Gonçalves, John Guaschi. 2006-03-15. The quaternion group as a subgroup of the sphere braid groups. https://doi.org/10.1112/blms%2Fbdl041

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