Characteristic 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: characteristic subgroup
View other analogues of characteristic 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 characteristic subloop if it satisfies the following equivalent conditions:

1. Every automorphism of the algebra loop sends the subloop to within itself.
2. Every automorphism of the algebra loop restricts to an automorphism of the subloop.

Relation with other properties

Incomparable properties

• Normal subloop: For full proof, refer: Characteristic not implies normal in algebra loops, Normal not implies characteristic in algebra loops