# Prove that every irreducible real representation of an abelian group is one or two dimensional. [closed]

Knowing the following theorem: " Every irreducible complex linear representation of an abelian group is one-dimensional " how can I prove the question mentioned in the title ..... Could anyone help me Please?

## closed as off-topic by YiFan, Leucippus, Cesareo, Shailesh, Eevee TrainerFeb 20 at 0:59

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But now I claim that every real representation arises this way: We know that every representation of $$G$$ over $$\mathbb{R}$$ or $$\mathbb{C}$$ appears inside the corresponding regular representation $$\mathbb{R}[G]$$ or $$\mathbb{C}[G]$$, but as a real representation $$\mathbb{C}[G] = \mathbb{R}[G] + i\mathbb{R}[G]$$ so every irreducible real representation appears inside the restriction of an irreducible complex representation.