Permutation-like matrix groups
Let \(\mathcal{G}\subset \mathbb{C}^{n\times n}\) be a finite group of matrices. If every \(X\in\mathcal{G}\) is similar to a permutation matrix, then \(\mathcal{G}\) is called a permutation-like group. The author investigates if a permutation-like group is equivalent to a group of permutation matrices. He finds counterexamples, but he has an affirmative answer under certain conditions, in particular for \(n=3\) and \(5\).
scientific article; zbMATH DE number 5141629