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Keywords = dihedralizable gyrogroup

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21 pages, 598 KB  
Article
On Dihedralized Gyrogroups and Their Cayley Graphs
by Rasimate Maungchang and Teerapong Suksumran
Mathematics 2022, 10(13), 2276; https://doi.org/10.3390/math10132276 - 29 Jun 2022
Cited by 8 | Viewed by 1852
Abstract
The method of constructing the generalized dihedral group as a semidirect product of an abelian group and the group Z2 of integers modulo 2 is extended to the case of gyrogroups. This leads to the study of a new class of gyrogroups, [...] Read more.
The method of constructing the generalized dihedral group as a semidirect product of an abelian group and the group Z2 of integers modulo 2 is extended to the case of gyrogroups. This leads to the study of a new class of gyrogroups, which includes generalized dihedral groups and dihedral groups as a special case. In this article, we show that any dihedralizable gyrogroup can be enlarged to a dihedralized gyrogroup. Then, we establish algebraic properties of dihedralized gyrogroups as well as combinatorial properties of their Cayley graphs. Full article
(This article belongs to the Special Issue Combinatorial Algebra, Computation, and Logic)
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