Right-transitively normal subloop

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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: normal subloop
View other analogues of normal subloop | View other analogues in algebra loops of subgroup properties (OR, View as a tabulated list)

Definition

A subloop of an algebra loop is termed a right-transitively normal subloop or a transitively normal subloop if every normal subloop of the subloop in a normal subloop of the whole loop.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Direct factor of a loop Central factor of a loop|FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Normal subloop