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01229nam a2200205Ia 4500 |
| 001 |
10.3390-math10132276 |
| 008 |
220718s2022 CNT 000 0 und d |
| 020 |
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|a 22277390 (ISSN)
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| 245 |
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|a On Dihedralized Gyrogroups and Their Cayley Graphs
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|b MDPI
|c 2022
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| 856 |
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|z View Fulltext in Publisher
|u https://doi.org/10.3390/math10132276
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|a 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. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
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|a Cayley graph
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|a dihedralizable gyrogroup
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|a dihedralized gyrogroup
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|a semidirect product
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|a skew left loop property
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|a Maungchang, R.
|e author
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|a Suksumran, T.
|e author
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| 773 |
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|t Mathematics
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