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

• # Fulltext

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

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

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019