Commutative loop

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This article defines a property that can be evaluated for a loop.
View other properties of loops
ANALOGY: This is an analogue in loop of a property encountered in group. Specifically, it is a loop property analogous to the group property: abelian group
View other analogues of abelian group | View other analogues in loops of group properties (OR, View as a tabulated list)

Definition

A loop is termed a commutative loop or abelian loop if its binary operation is a commutative binary operation, i.e., it is a commutative magma under its multiplication.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Commutative Moufang loop
Abelian group

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Commutative magma
Flexible loop