- #1

tomkoolen

- 40

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Member warned about posting without the HW template

The question: Let f: G -> H be a homomorphism of groups with ker(f) finite, the number of elements being n. Show that the inverse image is either empty or has exactly n elements.

My work so far:

Let h be eH (identity on H). Then the inverse image is ker(f) so has n elements, which makes it empty when n = 0.

I know how to do this for eH but how for all other y in H?

My work so far:

Let h be eH (identity on H). Then the inverse image is ker(f) so has n elements, which makes it empty when n = 0.

I know how to do this for eH but how for all other y in H?