Irreducible groups with submultiplicative spectrum
Let \({\mathcal J}_n\) be a finite group of \(n\times n\) matrices. The spectrum \(\sigma\) is submultiplicative on \({\mathcal J}_n\) if \(\sigma(ST)\subseteq\sigma(S)\sigma(T)=\{\lambda\mu:\lambda\in\sigma(S), \mu\in\sigma(T)\}\) for every \(S,T \in {\mathcal J}_n\). The author proves the existence of irreducible groups with submultiplicative spectrum for every even \(n\) which is divisible by 8. Two examples of such groups are constructed. It is shown that every group of \(2\times 2\) and \(4\times 4\) matrices is reducible.
scientific article; zbMATH DE number 2081758