T-group (mathematics)

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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 abelian group and 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 solvable T-group is metabelian.