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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 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 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. (en)
- Т-группа — группа, в которой отношение нормальности на множестве всех её подгрупп транзитивно. (ru)
- Т-група — група, в якій відношення нормальності на множині її підгруп транзитивне. (uk)
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- 1718 (xsd:nonNegativeInteger)
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- Т-группа — группа, в которой отношение нормальности на множестве всех её подгрупп транзитивно. (ru)
- Т-група — група, в якій відношення нормальності на множині її підгруп транзитивне. (uk)
- 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. (en)
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- T-group (mathematics) (en)
- Т-группа (математика) (ru)
- Т-група (математика) (uk)
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