Let G be a semisimple, simply connected algebraic group defined over ℝ. The set of real points G of G is not necessarily topologically simply connected, in which case G admits a nontrivial covering group. We give simple uniform proofs of several basic properties of real nonlinear groups, in particular, a simple criterion for when such a cover exists. Some of these properties were previously known from a case-by-case check based on the classification of real groups and their covers.

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