Structure of finite, minimal nonabelian groups and triangularization.
Using classical results of \textit{G. A. Miller} and \textit{H. C. Moreno} [Trans. Am. Math. Soc. 4, 398-404 (1903; JFM 34.0173.01)], the irreducible representations of finite, minimal non-Abelian groups are explicitly described and further results about these groups are derived. These are used to provide new answers to questions of the following form: If \(f\) is a homogeneous polynomial in two non-commuting variables, what conditions can be imposed so that whenever, for all \(A\), \(B\) in a semigroup of complex matrices (or compact operators on a Banach space), \(f(A,B)\) is ``small'' in some sense (e.g. is zero, nilpotent, quasi-nilpotent etc.), then the semigroup is triangularizable, or at least reducible?
scientific article; zbMATH DE number 5529490