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In this article, we discuss the Grothendieck group completion (GGC) of agyrogroup. Consequently, we show that there is a one to one correspondencebetween actions and representations of a gyrogroup, and actions andrepresentations of its Grothendieck group completion. We also introduce theconcept of an action of a right gyrogroup.

Gyrogroup through its Grothendieck Group Completion and Right gyrogroup action