Semi-cross product and extension theory of gyrogroups [Articol]

Abstract

We present the concept of a semi-cross product between a group and a gyrogroup, offering a means to construct a broader range of gyrogroups. Also, we develop the Schrier’s extension theory of gyrogroups. Consequently, we prove that a 2-fold extension feg ! H ! G ! K ! feg of a group H by a gyrogroup K splits if and only if G is a semi-cross product of H and K. Furthermore, we establish an equivalence between the category GEXT of group-gyro extensions, and the category GFAC of group-gyro factor systems.