Left Bruck loop

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This article defines a property that can be evaluated for a loop.
View other properties of loops

Definition

Bruck-Bol definition

A loop is said to be a left Bruck loop or left K-loop or left gyrocommutative gyrogroup if it satisfies the following conditions:

Gyrogroup definition

A gyrogroup (G,*) with gyration map \operatorname{gyr} is termed a left Bruck loop or left K-loop or left gyrocommutative gyrogroup if it satisfies the following identity called gyrocommutativity:

a * b = \operatorname{gyr}[a,b](b * a)

Relation with other properties

Weaker properties

References

External links