For many years, it was believed that the solvability of the integrability problem for a transitive Lie pseudogroup depends only on the local solvability of linear differential operators arising from the abelian quotients in Guillemin's Jordan-Hölder decomposition for the transitive Lie algebra associated to the pseudogroup. We provide an example of a transitive pseudogroup for which the integrability problem is not solvable and whose corresponding Jordan-Hölder sequence has only non-abelian quotients.
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