Subloop of index two

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

Definition

A subloop $S$ of a finite algebra loop $L$ is termed a subloop of index two if the size of $S$ is half that of $L$.

Relation with other properties

Weaker properties

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