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We give a general constructive proof for hierarchical coordinatizations(Lagrange Decompositions) of permutation groups. The generalization originatesfrom the investigation of how the subgroup chains of finite permutation groupsyield different coordinate systems. The study is motivated by the practicalneeds and the verification of an existing computational implementation. Largescale machine calculated examples are also presented.

Subgroup Chains and Lagrange Coordinatizations of Finite Permutation Groups