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mehtamonica
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The dihedral group Dn of order 2n has a subgroup of rotations of order n and a subgroup of order 2. Explain why Dn cannot be isomorphic to the external direct product of two such groups.
Please suggest how to go about it.
If H denotes the subgroup of rotations and G denotes the subgroup of order 2.
G = { identity, any reflection} ( because order of any reflection is 2)
I can see that order of Dn= 2n = order of external direct product
Please suggest how to go about it.
If H denotes the subgroup of rotations and G denotes the subgroup of order 2.
G = { identity, any reflection} ( because order of any reflection is 2)
I can see that order of Dn= 2n = order of external direct product