• Diagrams for Certain Quotients of $PSL(2, \mathbb{Z}[i])$

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      https://www.ias.ac.in/article/fulltext/pmsc/124/03/0291-0299

    • Keywords

       

      Bianchi group; Picard group; coset diagrams; quadratic number fields.

    • Abstract

       

      Actions of the Picard group $PSL(2,\mathbb{Z}[i])$ on $PL(F_p)$, where $p\equiv 1(\mathrm{mod} 4)$, 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 $PL(F_p)$. The conditions of existence of fixed points of the transformations are evolved. It is further proved that the action of the Picard group on $PL(F_p)$ is transitive. A code in Mathematica is developed to perform the calculation.

    • Author Affiliations

       

      Qaiser Mushtaq1 Awais Yousaf1

      1. Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 144000, Pakistan
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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