2-powered nilpotent group
This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: 2-powered group and nilpotent group
View other group property conjunctions OR view all group properties
Definition
A group is termed a 2-powered nilpotent group if it is both a 2-powered group (i.e., every element has a unique square root) and a nilpotent group.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| rationally powered nilpotent group | |FULL LIST, MORE INFO | |||
| Baer Lie group | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| 2-powered group | |FULL LIST, MORE INFO | |||
| 2-torsion-free nilpotent group | |FULL LIST, MORE INFO | |||
| nilpotent group | |FULL LIST, MORE INFO |