# Characteristic subloop

From Groupprops

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:

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