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Thread: Homomorphic images of D3.

  1. May 9th 2009, 03:58 PM #1
    o&apartyrock
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    Homomorphic images of D3.

    What are all the homomorphic images of D3 (up to isomorphism)?
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  2. May 9th 2009, 04:07 PM #2
    NonCommAlg
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    Quote Originally Posted by o&apartyrock View Post

    What are all the homomorphic images of D3 (up to isomorphism)?
    the kernel of such homomorphism is a normal subgroup of D_3. now D_3 has only 3 normal subgroups: (1), D_3, and a subgroup of order 3. so the homomorphic images are (1), \ D_3 and \mathbb{Z}/2\mathbb{Z}.
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