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:

• 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.

The solvable T-groups were characterized by

• ISBN 978-0-387-94461-6
• Ballester-Bolinches, Adolfo; Esteban-Romero, Ramon; Asaad, Mohamed (2010), Products of Finite Groups, Walter de Gruyter,
  ISBN 978-3-11-022061-2

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