Computing normalizers of tiled orders in \(M_n(k)\) (Q6165855)

If \(k\) is a non-Archimedean local field with \(R\) its valuation ring, then an order \(\Gamma\) in \(M_n(K)\) is a full \(R\)-lattice that is a subring containing the multiplicative identity in \(M_n(K)\) with \(\Gamma \otimes_R k = M_n(k).\) The order is tiled if it contains a conjugate of the ring \(diag(R,R,\dots,R).\) The normalizer of \(\Gamma\) is \({\mathcal N}(\Gamma) = \{ \xi \in GL_n(k) \ | \ \xi \Gamma \xi^{-1} = \Gamma \}.\) The author gives a five part algorithm to determine the normalizers of tiled orders in matrix algebras. For the entire collection see [Zbl 1416.11009].