Question

Asked Oct 25, 2019

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Step 1

Let G and G’ are any groups and ** f** is a homomorphism from

Step 2

Image and kernel of a group both are the subgroup of the group,

- The kernel of
, written*f*, is the set of elements*ker f**g**∈*such that*G**f(g) = 1.* - The image of
, written*f*, is the set of elements of*im f*of the form*H*for some*f(g)**g**∈**G.*

Now if** f** is a homomorphism of a group G to G’ then the image of f is a subgroup of H, and the kernel of

Now let’s show that ker f is a normal subgroup of G. Given an element x ∈ G and an element g ∈ ker f , we have

Step 3

The normal subgroup of the S3 and co...

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