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    Injections and Surjections

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    .....is a commutative diagram of groups and that the rows are exact,... being homomorphisms.
    Prove that
    (a) if and are surjections and is an injection, then is an injection.
    (b) if , and are injections, then is an injection.

    2. For a group extension
    {e} B H G {e}

    Prove that G ~ H/ (B).

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    Solution Summary

    Injections and Surjections are investigated. The solution is detailed and well presented.