Matrix groups with independent spectra Original Research Article

The article deals with triangularizability of a group of matrices over an algebraically closed field F with characteristic 0 under the assumption that the spectra of elements of the group satisfy an independency condition on their multiplicative orders and transcendental independency. Let p be a prime number and let matrix A be similar to a triangular matrix with diagonal entries λ1,…,λr,μ1,…,μs. If for i≠j the orders of λi and λj are finite with greatest common divisor dividing p and μ1,…,μs are transcendently independent over Q, we say that the matrix A has the p-property. The main result in this paper is that every matrix group consisting of matrices with the 2-property is triangularizable, which is a generalization of the result for a group with spectra in the set {1,−1} (see [1]). Some remarks on general prime p are also given.