Products of cyclic similarity classes in the groups \(\text{GL}_n(F)\)
Let \(\text{SL}_n(F)\) and \(\text{PSL}_n(F)\) denote the special linear and the projective special linear group, respectively. Assume \(|F|\geq 4\). The author shows that the group \(G=\text{PSL}_n(F)\) has a conjugacy class \(C\) such that \(C^2=G\). Further, if \(A\in\text{SL}_n(F)\), then \(A\) is a product of three cyclic unipotent matrices, if \(A\) is nonscalar, then it is a product of two cyclic unipotent matrices. These results are obtained as consequences of a factorization of any nonscalar matrix into two cyclic matrices having prescribed Jordan canonical form.
scientific article; zbMATH DE number 614118
scientific article