T-group (mathematics)

In mathematics, in the field of group theory, a T-group is a group in which the property of normality is transitive, that is, every subnormal subgroup is normal. Here are some facts about T-groups:
The solvable T-groups were characterized by Wolfgang Gaschütz as being exactly the solvable groups "G" with an abelian normal Hall subgroup "H" of odd order such that the quotient group "G"/"H" is a Dedekind group and "H" is acted upon by conjugation as a group of power automorphisms by "G".
A PT-group is a group in which permutability is transitive. A finite T-group is a PT-group.