Gyrotransversals of Order p3

Abstract

In this paper, we compute the isomorphism classes of gyrotransversals of order p3 corresponding to a fixed subgroup of order p in the group Zp⋉Zp3, where p is an odd prime. This yields a lower bound for the number of right gyrogroups of order p3 upto isomorphism. In addition, we obtain a lower bound for the non-isomorphic right gyrogroups of order p3 of nilpotency class 2.

Key words and phrases. Gyrotransversal, Right gyrogroup, Cauchy-Frobenius Formula, Right loop.

2010 Mathematics Subject Classification. 20N05