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Что (кто) такое T-group (mathematics) - определение
GROUP IN WHICH EVERY SUBNORMAL SUBGROUP IS NORMAL
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:
Trow
AMERICAN PUBLICLY OWNED INVESTMENT FIRM
T. Rowe Price Group; T. Rowe Price Group, Inc.; Rowe Price; T Rowe Price Group Inc; T. Rowe Price Group Inc.; T Rowe Price; TROW
A trow was a type of cargo boat found in the past on the rivers Severn and Wye in Great Britain and used to transport goods.
Trow
AMERICAN PUBLICLY OWNED INVESTMENT FIRM
T. Rowe Price Group; T. Rowe Price Group, Inc.; Rowe Price; T Rowe Price Group Inc; T. Rowe Price Group Inc.; T Rowe Price; TROW
Википедия
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 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.
