Subgroup of nilpotent group
This article describes a property that arises as the conjunction of a subgroup property: subgroup with a group property imposed on the ambient group: nilpotent group
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup
Definition
The term subgroup of nilpotent group is used for a situation of a subgroup of a group where the whole group is a nilpotent group.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| subgroup of abelian group | |FULL LIST, MORE INFO | |||
| normal subgroup of nilpotent group | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| hypernormalized subgroup | |FULL LIST, MORE INFO | |||
| subnormal subgroup | nilpotent implies every subgroup is subnormal | |FULL LIST, MORE INFO | ||
| subgroup of solvable group | nilpotent implies solvable | |FULL LIST, MORE INFO |