Finite simple groups the nilpotent residuals of all of whose subgroups are TI-subgroups

Let G be a finite group. A subgroup H of G is called a TI -subgroup of G if H ∩ H x = 1 or H for all x ∈ G . G N = ⋂ { N ⊴ G | G / N is nilpotent } is called the nilpotent residual of G . In this paper, we show that a non-abelian finite simple group the nilpotent residuals of all of its subgroups are TI -subgroups is isomorphic to either P S L ( 2 , 2 p ) for some prime p , to PSL (2, 7) or to the Suzuki group S z ( 2 p ) for some odd prime p .