**Authors:** Q. Mushtaq and U. Shuaib

### Abstract

We investigate actions of a certain Bianchi group B=PSL

_{2}(O

_{2}) on the projective line over the finite field, K=PL(F

_{p}), by drawing coset diagrams. We prove that B acts on K only if p-2 is a perfect square in F

_{p}. We prove that the permutation group (emerging from this) of the action is a subgroup of A

_{p+1}, and describe how the connectors connect different fragments occuring in the coset diagrams of the action of B on K. We also show that the group each orbit after removing the connectors from these coset diagrams is isomorphic to A

_{4} and establish formulae to count the number of orbits for each p and prove that the action is transitive.

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