exploring‎ ‎the ‎algebraic‎ ‎properties‎ ‎of gyrosemigroups and a characterization of gyrosemigroups of order 2

‎a significant development in the field of gyrogroups was the introduction of the space of all relativistically admissible velocities‎, ‎which brought gyrogroups into the mainstream‎. ‎a group has various generalizations‎, ‎one of which is the notion of gyrogroups‎. ‎moreover‎, ‎for any pair (a‎, ‎b) in this structure‎, ‎there exists an automorphism gyr[a‎, ‎b] that fulfills left associativity and left loop property‎. ‎the motivation behind this study is to generalize gyrogroups and semigroups‎, ‎which has led to the introduction of gyrosemigroups‎. ‎accordingly‎, ‎in this paper‎, ‎some classes of gyrosemigroups are presented‎. ‎also‎, ‎all gyrosemigroups of order 2 are characterized‎. ‎furthermore‎, ‎the gyrosemigroups with an identity or a zero are studied‎.