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Lemma: Kernel and Image of a Group Homomorphism are Subgroups

Let \(f:(G,\ast)\mapsto (H,\cdot)\) a group homomorphism. Then it follows that

  1. The kernel \(\ker(f)\) is a subgroup of \(G\).
  2. The image \(\operatorname{im}(f)\) is a subgroup of \(H\).

| | | | | created: 2014-09-06 16:20:51 | modified: 2019-07-27 15:56:06 | by: bookofproofs | references: [696]

1.Proof: (related to "Kernel and Image of a Group Homomorphism are Subgroups")

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Bibliography (further reading)

[696] Kramer Jürg, von Pippich, Anna-Maria: “Von den natürlichen Zahlen zu den Quaternionen”, Springer-Spektrum, 2013