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Diagrams for certain quotients of PSL(2, Z[i])
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| Organization: | Quaid-i-Azam University |
| Department: | Department of Mathematics |
| Organization: | Quaid-i-Azam University |
| Department: | Department of Mathematics |
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| Proceedings of the Indian Academy of Sciences - Section A Part 3 Mathematical sciences |
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Actions of the Picard group PSL(2, Z[i]) on PL(Fp), where p ≡1(mod 4), are investigated through diagrams. Each diagram is composed of fragments of three types. A technique is developed to count the number of fragments which frequently occur in the diagrams for the action of the Picard group on PL(Fp). The conditions of existence of fixed points of the transformations are evolved. It is further proved that the action of the Picard group on PL(Fp) is transitive. A code in Mathematica is developed to perform the calculation.
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