Icosahedral Group and Classification of PSL(2, Z)-Orbits of Real Quadratic Fields
Reduced numbers play an important role in the study of modular group action on the PSL2,ℤ-subset of Qm/Q. For this purpose, we define new notions of equivalent, cyclically equivalent, and similar G-circuits in PSL2,ℤ-orbits of real quadratic fields. In particular, we classify PSL2,ℤ-orbits of Qm/Q=∪...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/9568254 |
| Summary: | Reduced numbers play an important role in the study of modular group action on the PSL2,ℤ-subset of Qm/Q. For this purpose, we define new notions of equivalent, cyclically equivalent, and similar G-circuits in PSL2,ℤ-orbits of real quadratic fields. In particular, we classify PSL2,ℤ-orbits of Qm/Q=∪k∈NQ∗k2m containing G-circuits of length 6 and determine that the number of equivalence classes of G-circuits of length 6 is ten. We also employ the icosahedral group to explore cyclically equivalence classes of circuits and similar G-circuits of length 6 corresponding to each of these ten circuits. This study also helps us in classifying reduced numbers lying in the PSL2,ℤ-orbits. |
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| ISSN: | 2314-4629 2314-4785 |