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This paper reports a study on the problem of the blind simultaneous extraction of specific groups of independent components from a linear mixture. This paper first presents a general overview and unification of several information theoretic criteria for the extraction of a single independent component. Then, our contribution fills the theoretical gap that exists between extraction and separation by presenting tools that extend these criteria to allow the simultaneous blind extraction of subsets with an arbitrary number of independent components. In addition, we analyze a family of learning algorithms based on Stiefel manifolds and the natural gradient ascent, present the nonlinear optimal activations (score) functions, and provide new or extended local stability conditions. Finally, we illustrate the performance and features of the proposed approach by computer-simulation experiments.