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

Proceedings Mathematical Sciences

Awais Yousaf¹  Qaiser Mushtaq² 

[1] $$;Department of Mathematics, Quaid-i-Azam University 0, Islamabad 000, Pakistan$$

关键词: Bianchi group;    Picard group;    coset diagrams;    quadratic number fields.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Actions of the Picard group $PSL(2,mathbb{Z}[i])$ on $PL(F_p)$, where $p≡ 1(mathrm{mod} 4)$, 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.

【 授权许可】

Unknown