Gyrotransversals of order p2 [Articol]

Abstract

The isomorphism classes of gyrotransversals of order p2 is calculated in the group Zp n Zp2 corresponding to a fixed subgroup of order p, where p is an odd prime. As a consequence, a lower bound for the non-isomorphic right gyrogroups of order p2 is obtained. Also, we obtain a lower bound for the non-isomorphic right gyrogroups of order p2 of nilpotency class 2.