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The residual limit points of finitely generated Kleinian groups are classified into two types: the first kind and the second kind. To each point of the second kind, Abikoff associated a web subgroup. We shall classify the points of the first kind into two types and associate to each point of one type a finitely generated subgroup, the nest subgroup. To the points of the other type we shall give a significance showing that they are important for the sets of generators.doi:10.1090/s0002-9947-1983-0697083-5 fatcat:h5f6wkgvuzbpxo7emras5qks2u