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.