On the holomorph of finite semisimple groups

Abstract

Given a finite nonabelian semisimple group $G$, we describe those groups that have the same holomorph as $G$, that is, those regular subgroups $N\simeq G$ of $S(G)$, the group of permutations on the set $G$, such that $N_{S(G)}(N)=N_{S(G)}(\rho(G))$, where $\rho$ is the right regular representation of $G$.