Nilpotent implies every subgroup is subnormal
This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., nilpotent group) must also satisfy the second group property (i.e., group in which every subgroup is subnormal)
View all group property implications | View all group property non-implications
Get more facts about nilpotent group|Get more facts about group in which every subgroup is subnormal
- Hypocentral implies every subgroup is descendant: In particular, since residually nilpotent implies hypocentral, every subgroup of a residually nilpotent group is descendant.
The converse is not true in general, but is true for finite groups:
- Every subgroup is subnormal not implies nilpotent
- Equivalence of definitions of finite nilpotent group