Cocentral 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: cocentral subgroup
View other analogues of cocentral 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 cocentral subloop if $SZ=L$ where $Z=Z(L)$ denotes the center of $L$.

Relation with other properties

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
central factor of a loop
normal subloop		cocentral implies normal for loops