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Under some regularity conditions one proves that quotients and kernels of infinitesimal analytic Lie pseudo-groups by invariant fiberings are again infinitesimal Lie pseudo-groups. The regularity conditions are shown to be necessary and sufficient if one wishes both quotient and kernel to be infinitesimal Lie pseudo-groups. One defines and proves the existence of the quotient of an infinitesimal Lie pseudo-group by a normal sub-pseudo group. An equivalence relation for germs of infinitesimal Lie...
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