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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 simple 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 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. ==References== * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「T-group (mathematics)」の詳細全文を読む スポンサード リンク
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