On Dihedralized Gyrogroups and Their Cayley Graphs

Rasimate Maungchang and Teerapong Suksumran
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Rasimate Maungchang: School of Science, Walailak University, Nakhon Si Thammarat 80160, Thailand
Teerapong Suksumran: Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2022, vol. 10, issue 13, 1-21

Abstract: The method of constructing the generalized dihedral group as a semidirect product of an abelian group and the group Z 2 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.

Keywords: dihedralizable gyrogroup; dihedralized gyrogroup; Cayley graph; semidirect product; skew left loop property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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