Would you please help me in how to solve these questions :
A- Let $H$ be a subgroup of a finite group $G$.Let $\alpha$ and $\beta$ be class function of $G$ and $H$ respectively. Prove that $Ind^{G}_{H} (\beta . Res^{G}_{H})= \alpha .Ind^{G}_{H}(\beta) $
B- Show that
1.Each element in $SU(n)$ conjugate to a diagonal matrix.
- Every character of $SU(n)$ is uniquely determined by its restriction to subgroup $T$ consisting of all diagonal matrices whose diagonal coefficients have absolute value 1.
Many thanks.