Construction of gyrogroups via group actions by automorphism

This paper deals with an admissible AR-group, which is a group admitting an action on itself by automorphism (or, alternatively, an automorphism representation on itself) satisfying a certain nice property. Then it is shown that this group gives rise to a nonassociative group-like structure called a gyrogroup via the method of forming semidirect products. Several families of admissible AR-groups are also determined.