Fully invariant subloop

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 loop of a property encountered in group. Specifically, it is a subloop property analogous to the subgroup property: fully invariant subgroup
View other analogues of fully invariant subgroup | View other analogues in loops of subgroup properties (OR, View as a tabulated list)

Definition

A subloop of an algebra loop is termed a fully invariant subloop if it is invariant under all the endomorphisms of the loop.

Relation with other properties

Weaker properties

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