On a Generalisation of Finite T-Groups

Let sigma = {sigma(i)vertical bar i is an element of I} be some partition of all primes P and G a finite group. A subgroup H of G is said to be sigma-subnormal in G if there exists a subgroup chain H = H-0 <= H-1 <= ... <= H-n = G such that either Hi-1 is normal in H-i or H-i /(Hi-1)(Hi) is a finite sigma(j)-group for some j is an element of I for i = 1, ... , n. We call a finite group G a T-sigma-group if every s-subnormal subgroup is normal in G. In this paper, we analyse the structure of the T-sigma-groups and give some characterisations of the T-sigma-groups.