A Generalization of Szep’s Conjecture for Almost Simple Groups

Abstract We prove a natural generalization of Szep’s conjecture. Given an almost simple group G with socle not isomorphic to orthogonal having Witt defect zero, we classify all possible elements $$x,y\in G\setminus \{1\}$$ x , y ∈ G \ { 1 } $$G=\textbf{N}_G(\langle x\rangle )\textbf{N}_G(\langle y\rangle )$$ = N ( ⟨ ⟩ ) , where are denoting by $$\textbf{N}_G(\langle and the normalizers cyclic subgroups $$\langle $$ . As consequence this result, $$G=\textbf{C}_G(x)\textbf{C}_G(y)$$ C