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Definition: Group Homomorphism

A homomorphism \(f:G\rightarrow H\) is called a group homomorphism, if \((G,\ast)\) and \((H,\cdot)\) are two groups.

| | | | | created: 2014-06-09 21:19:50 | modified: 2020-06-28 10:02:44 | by: bookofproofs | references: [677]

1.Example: Examples of Group Homomorphisms

2.Proposition: Properties of a Group Homomorphism

3.Example: Examples of Properties of Group Homomorphisms

4.Lemma: Kernel and Image of Group Homomorphism

5.Example: Examples of Kernels and Images of Group Homomorphisms

6.Lemma: Kernel and Image of a Group Homomorphism are Subgroups

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Bibliography (further reading)

[677] Modler, Florian; Kreh, Martin: “Tutorium Algebra”, Springer Spektrum, 2013