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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:

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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?

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

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