Abstract:

The solution of the following problem by G. Malle, J.~Saxl and T. Weigel has been completed for the projective symplectic groups $PSp_4(q)$, (see also question 14.69c) from the Kourovka Notebook). For each finite simple non-Abelian group $G$, find $n_c(G)$ which is the minimal number of generating conjugate involutions whose product is equal to 1. It turns out that if $G=PSp_4(q)$, then $n_c(G)=5$ for $q\neq 2,3$, $n_c(G)=6$ for $q=3$, and $n_c(G)=10$ for $q=2$ (in this case, the group $G$ is not simple).