Geometry of Gyrogroups via Klein’s Approach

Using Klein's approach, geometry can be studied in terms of a space points and group transformations that space. This allows us to apply algebraic tools studying mathematical structures. In this article, we follow approach study the $(G, \mathcal{T})$, where $G$ is an abstract gyrogroup $\mathcal{T}$ appropriate containing all gyroautomorphisms $G$. We focus on $n$-transitivity gyrogroups also give few characterizations coset spaces minimally invariant sets. then prove collection open balls equal radius set \Gamma_m)$ for any normed $G$, $\Gamma_m$ suitable isometries