Solvable Moufang loop
From Groupprops
This article defines a property that can be evaluated for a loop.
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This is a variation of solvable group|Find other variations of solvable group |
Contents
Definition
A solvable Moufang loop is a loop that is both a solvable loop and a Moufang loop.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| solvable group | ||||
| nilpotent Moufang loop |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Moufang loop of group type (at least for finite Moufang loops) | all composition factors are groups |
