On the holomorph of finite semisimple groups

Abstract

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 ≃ G {N\simeq G} of S ⁢ ( G ) {S(G)} , the group of permutations on the set G, such that N S ⁢ ( G ) ⁢ ( N ) = N S ⁢ ( G ) ⁢ ( ρ ⁢ ( G ) ) {N_{S(G)}(N)=N_{S(G)}(\rho(G))} , where ρ is the right regular representation of G.