Nilpotent Moufang loop
From Groupprops
This article defines a property that can be evaluated for a loop.
View other properties of loops
This is a variation of nilpotent group|Find other variations of nilpotent group |
Contents
Definition
A nilpotent Moufang loop is a loop that is both a nilpotent loop and a Moufang loop.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Nilpotent group | ||||
| Moufang loop of prime power order | Moufang loop whose order (size) is a prime power | prime power order implies nilpotent for Moufang loops |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Solvable Moufang loop |
