Generating Sets of Conjugate Involutions of Groups PSL.sub.n

G. Malle, J. Saxl, and T. Weigel in [Geom. Ded., 49, No. 1, 85-116 (1994)] formulated the following problem: For every finite simple non-Abelian group G, find the minimum number n.sub.c(G) of generators of conjugate involutions whose product equals 1. (See also Question 14.69c in [Unsolved Problems in Group Theory. The Kourovka Notebook, No. 20, E. I. Khukhro and V. D. Mazurov (Eds.), Sobolev Institute of Mathematics SO RAN, Novosibirsk (2022);