This article defines a property that can be evaluated for a subloop of a loop| View other such properties
ANALOGY: This is an analogue in algebra loop of a property encountered in group. Specifically, it is a subloop property analogous to the subgroup property: central subgroup
View other analogues of central subgroup | View other analogues in algebra loops of subgroup properties (OR, View as a tabulated list)
Note that any central subloop is an abelian group under the induced multiplication because the multiplication operation on it is associative.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|Normal subloop||Central factor of a loop|FULL LIST, MORE INFO|
|Nuclear subloop||contained in the nucleus|||FULL LIST, MORE INFO|