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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 kernel \(\ker(f)\) is a subgroup of \(G\).

Table of Contents

Proofs: 1

Mentioned in:

Explanations: 1
Proofs: 2 3 4

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References

Bibliography

1. Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013