# all one-dimensional representations of a group G (over algebraically closed field) can be obtained us one-dimensional representations of G/G'.

How can I prove that:

all one-dimensional representations of a group G (over algebraically closed field) can be obtained us one-dimensional representations of G/G'.

Do I have to use this definition to prove it:

And if I used this definition for the proof, How can this theorem applied to $$A_{4}/V$$ where $$V$$ is the klein 4 group and knowing that $$A_{4}/V$$ is isomorphic to $$Z_{3}$$? what is the kernel that V belongs to?

• Yes, you want to use the paragraph that follows "conversely" – Max Feb 20 at 10:14