Some studies on algebraic integers in $$\mathbb {Q} (i,\sqrt{3})$$ Q ( i , 3 ) by using coset diagram

Abstract

In this paper, we studied the action of Picard modular group $$PSL(2, \mathbb {Z} [i])$$ denoted by $$\Gamma $$ on the biquadratic field $$ \mathbb {Q} \left( i,\sqrt{3}\right) $$ . We found patern of algebraic integers formed by this action. To prove results we used coset diagrams for the action of $$\Gamma $$ on $$ \mathbb {Q} \left( i,\sqrt{3}\right) $$ , proponded by Graham Higman.