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Math Help - Abstract - Homomorphism

  1. #1
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    Abstract - Homomorphism

    Hi,

    Can anybody help with the following questions please?

    1. Find the homomorphic image of the group S3.

    2. Find two nonisomorphic extensions of Z 4 by Z 2.


    Can you explain any answers please as I'm finding it hard to get my head around homomorphisms?


    Thanks.


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  2. #2
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    Quote Originally Posted by jackiemoon View Post

    1. Find the homomorphic image of the group S3.
    Remember that the homomorphic image of S_3 is isomorphic to S_3 modulo the kernel of the homomorphism. Since the kernel must be a normal subgroup of S_3 it means that the kernel is either \{ e\}, A_3, S_3 and so the homomorphic image is either S_3, \mathbb{Z}_2, \text{ or }\mathbb{Z}_1.

    2. Find two nonisomorphic extensions of Z 4 by Z 2.
    I am not sure what you mean by this?
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