Construction of Right Gyrogroups

Abstract

Attempts have been made to introduce notion of class assigned functions k for a given group G and observed that it determines a right gyrogroup $$(G, o_k)$$ . It is also observes that $$(G, o_k)$$ will be a group if and only if G is a nilpotent group of class 2 and will be a gyrogroup for a nilpotent group of class 3, where $$k(x)=1$$ for all $$x\in G\setminus \{1\}$$ .