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.