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I am confused about the answers to the following question: Restriction to a normal subgroup

with the original question copied here:

Let $A$ be a normal subgroup of a finite group $G$ and $V$ an irreducible representation of $G$. Show that either $\text{Res}_A^G V$ is isotypic (a sum of copies of one irreducible representation of $A$) or that $V$ is induced from some proper subgroup of $G$.

I came across the same question in Lang's Algebra, however, Lang does not talk about torsion groups in the section nor is there mention of Clifford's theorem. Therefore, I was wondering if there was another, perhaps more fundamental, way to approach this question, as both answers are based off of other results.

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I would say this is just a reformulation of Clifford's Theorem, which is more or less what Geoff Robinson said in his previous answer to the question. – Derek Holt Nov 28 '12 at 9:40

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