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: * Every simple group is a T-group. * Every quasisimple group is a T-group. * Every abelian group is a T-group. * Every Hamiltonian group is a T-group. * Every nilpotent T-group is either abelian or Hamiltonian, because in a nilpotent group, every subgroup is subnormal. * Every normal subgroup of a T-group is a T-group. * Every homomorphic image of a T-group is a T-group. * Every solvable T-group is metabelian.