The quaternion group as a subgroup of the sphere braid groups
Geometric Topology
2011-11-09 v1 Group Theory
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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Cite
@article{arxiv.math/0603377,
title = {The quaternion group as a subgroup of the sphere braid groups},
author = {Daciberg Lima Gonçalves and John Guaschi},
journal= {arXiv preprint arXiv:math/0603377},
year = {2011}
}
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3 pages