The Covering Number of the GroupPSLn(F) Original Research Article

LetGbe the groupPSLn(F), wheren≥3,Fis a field, and F≥4. Assume, further, that ifn=3, thenFis either finite or algebraically closed. Given an integerkand a subsetAsubset of or equal toG, denoteAk={a1a2···aka1, a2,…,akset membership, variantA}. Denote by cn(G) the minimal value ofksuch thatCk=Gfor every nontrivial conjugacy classCofG. It is shown that cn(G)=n. Related results on factorizations of matrices inGLn(F) andSLn(F) are also discussed.