Question

Asked Apr 21, 2019

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Let φ : G → H be a group homomorphism.

(a) Prove that Ker(φ) is a normal subgroup of G.

(a) Prove that Im(φ) is a subgroup of G. Is it normal? When?

Step 1

To discuss normality of kernel and image under group homomorphisms,

Step 2

The kernel of a homomorphism is the set of all elements which are taken to the identity element and the image of a homomorphism is the set of all elements having pre-images .

Step 3

Proof that Kernel of a homomorphism is always a normal subgroup. T...

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