A remark on "A note on TI-subgroups of finite groups"

Abstract

Indian Acad. Sci. (Math. Sci.) 122 (2012) 75-77.] proved that Theorem 2.4. Let G be a non-nilpotent NATI-group. Then one of the followings holds: (1) G = NH is a Frobenius group with a kernel N and a complement H, where N is the minimal normal subgroup of G and H is either a cyclic group or a product of Q 8 with a cyclic group of odd order. (2) Z(G) = 1, G is a quasi-Frobenius group with an abelian complement, and for any non-abelian subgroup H of G, H is normal in G, or H is a product of Q 8 with a cyclic group of odd order.