THE COVERING NUMBER OF THE GROUP PSL(N)(F)

摘要

Let G be the group PSL(n)(F), where n greater than or equal to 3, F is a field, and F greater than or equal to 4. Assume, further, thai if n = 3, then F is either finite or algebraically closed, Given an integer k and a subset A subset of or equal to G, denote A(k) = {a(1)a(2) ... a(k) (1),a(2), ..., a(k) is an element of A}. Denote by cn(G) the minimal value of k such that C-k = G for every nontrivial conjugacy class C of G. ir is shown that cn(G) = n. Related results on factorizations of matrices in GL(n)(F) and SL(n)(F) are also discussed. (C) 1996 Academic Press, Inc. [References: 22]