Solvable Moufang loop: Difference between revisions
| Line 23: | Line 23: | ||
! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions | ! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions | ||
|- | |- | ||
| [[ | | [[Moufang loop of group type]] (at least for [[finite Moufang loop]]s)|| all composition factors are groups || || || | ||
|} | |} | ||
Latest revision as of 03:49, 20 August 2011
This article defines a property that can be evaluated for a loop.
View other properties of loops
This is a variation of solvable group|Find other variations of solvable group |
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 |