On finite solvable groups in which normality is a transitive relation

Finite groups with some NR-subgroups or $${\mathcal{H}}$$ -subgroups

“…A subgroup of G is called s-permutable in G if it permutes with all Sylow subgroups of G. A group G is said to be a PST-group if s-permutability is a transitive relation in G. By a result of Kegel ( [4], Theorem 1.2.14(3)) PST-groups are exactly those groups where all subnormal subgroups are s-permutable. In the literature there are several characterizations of finite soluble T -groups, PT -groups and PST-groups (see [3][4][5][6]8]). …”

“…Bianchi, Gillio Berta Mauri, Herzog and Verardi ( [8], Theorem 10) proved a characterization of soluble T -groups by means of H-subgroups:…”

On Generalised Fc-Groups in Which Normality Is a transitive Relation

“…In their seminal papers, G. Zacher [22] (1952) and W. Gaschütz [7] (1957) described the structure of finite soluble T-groups. Later, many authors studied finite groups in which normality is transitive, and more characterisations were obtained (see for instance [1,2,3,9,10,14]) in terms of properties of subgroups. It turns out that every finite soluble T-group is aT-group (that is, a group in which every subgroup is a T-group).…”

On finite T-groups and the Wielandt subgroup

“…T-groups have been widely studied since the aforementioned papers by Zacher and Gaschü tz and the important contributions by Robinson [9] and Peng [7]. Characterizations of solvable T-groups are given, for instance, in [2], [3] and [1].…”