69 citations · 150 across the 12 of their papers we have counts for
8 papers · 1 filter
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…
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…