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| In [[mathematics]], the '''binary cyclic group''' of the ''n''-gon is the cyclic group of order 2''n'', <math>C_{2n}</math>, thought of as an [[group extension|extension]] of the cyclic group <math>C_n</math> by a [[cyclic group]] of order 2.
| | I'm Wolfgang (26) from Kaltenherberg, Switzerland. <br>I'm learning English literature at a local high school and I'm just about to graduate.<br>I have a part time job in a university.<br><br>Feel free to visit my homepage; home renovator - [http://www.homeimprovementdaily.com homeimprovementdaily.com] - |
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| It is the [[binary polyhedral group]] corresponding to the cyclic group.
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| In terms of binary polyhedral groups, the binary cyclic group is the preimage of the cyclic group of rotations (<math>C_n < \operatorname{SO}(3)</math>) under the 2:1 [[covering homomorphism]]
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| :<math>\operatorname{Spin}(3) \to \operatorname{SO}(3)\,</math> | |
| of the [[special orthogonal group]] by the [[spin group]].
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| As a subgroup of the spin group, the binary cyclic group can be described concretely as a discrete subgroup of the unit [[quaternion]]s, under the isomorphism <math>\operatorname{Spin}(3) \cong \operatorname{Sp}(1)</math> where [[Sp(1)]] is the multiplicative group of unit quaternions. (For a description of this homomorphism see the article on [[quaternions and spatial rotation]]s.)
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| ==See also==
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| *[[binary dihedral group]]
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| *[[binary tetrahedral group]]
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| *[[binary octahedral group]]
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| *[[binary icosahedral group]]
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| [[Category:Binary polyhedral groups|Cyclic]]
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| {{Abstract-algebra-stub}}
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Latest revision as of 03:22, 2 November 2014
I'm Wolfgang (26) from Kaltenherberg, Switzerland.
I'm learning English literature at a local high school and I'm just about to graduate.
I have a part time job in a university.
Feel free to visit my homepage; home renovator - homeimprovementdaily.com -