Let $E_{i,j}$ be the $n \times n$ elementary matrices. Let $G=GL_n(\mathbb{Z}_p)$. Let $T_G$ be the split maximal torus of $GL_n(\mathbb{Z}_p)$. Let $\Theta$ be the subgroup of $T_G$ consisting of matrices with all the diagonal entries in $\mu_{p-1}$, the $(p-1)^{th}$ roots of unity in $\mathbb{Z}_p$. Let $K$ be the group $\mathbb{Z}_p^{\times}I_n$, where $I_n$ is the identity matrix. Let $T_S$ be the split maximal torus of $SL_n(\mathbb{Z}_p)$. Let $P:=\{g \in T_S|g\equiv 1 (\mod p\mathbb{Z}_p)$. Then my questions are
1) Is the group $T_G/K\Theta P$ finite?
2) Is the group $T_G/KP$ finite?
Thanks in advance for help.