69 citations · 150 across the 12 of their papers we have counts for
13 papers
Geometry of gyrogroups via Klein's approach
Teerapong Suksumran
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 geom…
On transitivity and connectedness of Cayley graphs of gyrogroups
Rasimate Maungchang, Prathomjit Khachorncharoenkul, Kiattisak Prathom +1
In this work, we explore edge direction, transitivity, and connectedness of Cayley graphs of gyrogroups. More specifically, we find conditions for a Cayley graph of a gyrogroup to…
Frobenius reciprocity on the space of functions invariant under a group action
Teerapong Suksumran, Tanakorn Udomworarat
This article studies connections between group actions and their corresponding vector spaces. Given an action of a group on a nonempty set , we examine the space of s…
The isometry group of -dimensional Einstein gyrogroup
Teerapong Suksumran
The space of -dimensional relativistic velocities normalized to , is naturally associated with Ei…
An inequality related to Möbius transformations
Themistocles M. Rassias, Teerapong Suksumran
The open unit ball is endowed with Möbius addition defined by $$\mathbf{u}\oplus_M\mathbf{v} = \dfrac{…
On metric structures of normed gyrogroups
Teerapong Suksumran
In this article, we indicate that the open unit ball in -dimensional Euclidean space admits norm-like functions compatible with the Poincaré and BeltramiKlein…
Geometry of generated groups with metrics induced by their Cayley color graphs
Teerapong Suksumran
Let be a group and let be a generating set of . In this article, we introduce a metric on with respect to , called the cardinal metric. We then compare geom…
Extension of Maschke's theorem
Teerapong Suksumran
In the present article, we examine linear representations of finite gyrogroups, following their group-counterparts. In particular, we prove the celebrated theorem of Maschke for gy…
Special subgroups of gyrogroups: Commutators, nuclei and radical
Teerapong Suksumran
A gyrogroup is a nonassociative group-like structure modelled on the space of relativistically admissible velocities with a binary operation given by Einstein's velocity addition l…
Gyrogroup actions: A generalization of group actions
Teerapong Suksumran
This article explores the novel notion of gyrogroup actions, which is a natural generalization of the usual notion of group actions. As a first step toward the study of gyrogroup a…
Bi-gyrogroup: The group-like structure induced by bi-decomposition of groups
Teerapong Suksumran, Abraham A. Ungar
The decomposition of a group into a subset and a subgroup of induces, under general conditions, a group-like structure for , known as a gyrogroup. The fam…
Lagrange's Theorem for Gyrogroups and the Cauchy Property
Teerapong Suksumran, Keng Wiboonton
In this paper, we prove a version of Lagrange's theorem for gyrogroups and use this result to prove that gyrogroups of particular orders have the strong Cauchy property.
Isomorphism Theorems for Gyrogroups and L-Subgyrogroups
Teerapong Suksumran, Keng Wiboonton
We extend well-known results in group theory to gyrogroups, especially the isomorphism theorems. We prove that an arbitrary gyrogroup induces the gyrogroup structure on the sym…