Products of cyclic conjugacy classes in the groups PSL(n,F)

Abstract Let G be the group PSL(n,F), where F is a field and n ⩾ 3. If C is a conjugacy class of G, denote C-1 = {c-1∥c ∈ C}. The following is proved: (1) If C1, C2, C3 are cyclic conjugacy classes of G, then C1C2C3 ⊇ G - {1G}. (2) If F is algebraically closed and C1, C2 are cyclic conjugacy classes of G, then C1C2 = G if and only if C1 = C-12. Generalizations of these results, concerning factorizations of a given nonscalar invertible matrix as a product of two or three cyclic matrices, each lying in a prescribed conjugacy class of GL(n, F) [or SL(n,F], are discussed.