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Math Help - Hungerfold problem help

  1. #1
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    Hungerfold problem help

    12. A normal subgroup H of a group G is said to be a direct factor (direct summand if
    G is additive abelian) if there exists a (normal) subgroup K of G such that
    G = HX K.

    Prove that:

    (a) If H is a direct factor of K and K is a direct factor of G, then H is normal
    in G.
    (b) If H is a direct factor of G, then every homomorphism H —>G may be
    extended to an endomorphism G -> G. However, a monomorphism H -> G need
    not be extendible to an automorphism G —> G.

    Last edited by Mali_42; December 4th 2008 at 09:09 AM.
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