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IMI/Publicaţii/QRS/Ediţii/QRS v.21, n.2 (30), 2013/

Coset diagrams of the action of a certain Bianchi group on PL(Fp)

Authors: Q. Mushtaq and U. Shuaib

Abstract

We investigate actions of a certain Bianchi group B=PSL2(O2) on the projective line over the finite field, K=PL(Fp), by drawing coset diagrams. We prove that B acts on K only if p-2 is a perfect square in Fp. We prove that the permutation group (emerging from this) of the action is a subgroup of Ap+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 A4 and establish formulae to count the number of orbits for each p and prove that the action is transitive.

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