Finite Groups All of Whose Subgroups are P-Subnormal or TI-Subgroups

Let P be the set of all prime numbers. A subgroup H of a finite group G is said to be P-subnormal in G if there exists a chain of subgroups H=H-0 subset of H-1 subset of<middle dot><middle dot><middle dot>subset of Hn-1 subset of H-n=G such that eitherH(i-1)is normal inH(i)or|H-i:Hi-1|is a prime number for every i=1,2,...,n. A subgroup H of G is called a TI-subgroup if every pair of distinct conjugates of H has trivial intersection. The aim of this paper is to give a complete description of all finite groups in which every non-P-subnormal subgroup is a TI-subgroup