The paper 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 \(l_1,\dots,l_r\), \(m_1,\dots, m_s\). If for \(i\neq j\) the orders of \(l_i\) and \(l_j\) are finite with greatest common divisor dividing \(p\) and \(m_1,\dots, m_s\) are transcendently independent over \(\mathbb{Q}\), we say that the matrix \(A\) has the \(p\)-property.
The main result in the paper is that every matrix group consisting of matrices with the \(2\)-property is triangularizable. Some remarks on general prime \(p\) are also given.