[代數] direct factor
Def:
A normal subgroup H of a group G is said to be a direct factor
if there exists a (normal)subgroup K of G such that G=H×K
problem:
(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.
以上為Hungerford代數的習題
懇請板上高手協助 感謝!!!!
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