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