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Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
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Relationship between non-zero values of characters and normality in finite groups
Note: Let $G$ be a finite group and $H \leq G$. Then it is clear that if $H \unlhd G$, then $\chi(h) \neq 0$ for irreducible constituents $\chi$ of the permutation character $(1_H)^G$ and $h\in H$. T …