Subnormal 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: subnormal subgroup
View other analogues of subnormal subgroup | View other analogues in loops of subgroup properties (OR, View as a tabulated list)

Definition

A subloop $S$ of a loop $L$ is termed a subnormal subloop if there exists an ascending chain of subloops:

$S=A_{0}\leq A_{1}\leq \dots \leq A_{n}=L$

such that each $A_{i}$ is a normal subloop of $A_{i+1}$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
normal subloop				|FULL LIST, MORE INFO
2-subnormal subloop	normal subloop of normal subloop			|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Lagrange-like subloop in finite loop				|FULL LIST, MORE INFO