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Coset diagrams of the action of a certain Bianchi group on PL(Fp)
Authors: Q. Mushtaq and U. Shuaib
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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.Fulltext
– 0.33 Mb
Contents
- On Latin squares of polynomially complete quasigroups and quasigroups generated by shifts
- Hom-Bol algebras
- Ascending chain conditions on principal left and right ideals for semidirect products of ordered semigroups
- On regular medial division algebras
- Contractions of quasigroups and Latin squares
- On 2-absorbing semimodules
- Strong forms of orthogonality for sets of frequency hypercubes
- A still shorter axiom for trimedial quasigroups
- Clifford congruences on perfect semigroups
- E-disjunctive semigroups and idempotent pure congruences
- Groups with the same orders and large character degrees as PGL(2,9)
- Coset diagrams of the action of a certain Bianchi group on PL(Fp)
- Automorphisms of abelian n-ary groups
- Free products of dimonoids
