| 1. | The quaternion group is the smallest example of nilpotent non-abelian group.
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| 2. | The other non-abelian group of order 8 is the quaternion group " Q " 8.
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| 3. | The stabilizer of 4 points is the quaternion group.
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| 4. | Consider for example, the simple quaternion group, whose cycle graph is shown on the right.
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| 5. | This event marks the discovery of the quaternion group.
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| 6. | The generalized quaternion group of order 16 also forms a subgroup of 2 " O ".
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| 7. | A generalization due to Hall are the A-groups, those groups with dihedral and generalized quaternion groups.
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| 8. | They all have unit magnitude and therefore lie in the unit quaternion group Sp ( 1 ).
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| 9. | The quaternion group has five irreducible representations, and their dimensions are 1, 1, 1, 1, 2, respectively.
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| 10. | The quaternion group is a normal subgroup of the binary tetrahedral group U ( " H " ).
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