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Let G and H be two groups, f : G H a group morphism and K G a distinguished subgroup. Show that the following two
Let G and H be two groups, f : G H a group morphism and K G a distinguished subgroup. Show that the following two conditions are equivalent: (A) K Ker f (i.e. For all k K, f(k) = eH, the neutral of H). (B) There exists a group morphism : G/K H such that (x.K) = f(x).
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