On the characters of the group of upper-triangular matrices
The author shows that all complex characters of certain finite groups are monomial (groups with this property are called \(M\)-groups). The groups under consideration are defined as the groups of units of certain finite associative algebras. Let \(K\) be a finite field of \(q\) elements, and \(A\) a finite (dimensional) algebra over \(K\). Then \(A\) is called a \(DN\)-algebra if \(A/\text{Rad }A\) is a direct sum of copies of \(K\). The author proves that the group \(G(A)\) of units of \(A\) is an \(M\)-group, and that the degrees of complex characters of \(G(A)\) are of shape \(q^r(q-1)^s\) for some integers \(r,s\geq 0\).
scientific article; zbMATH DE number 954745