Permanence properties of -exact groups.
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The theory of matched pairs of groups is surveyed with special interest in applications to braided groups and quasitriangular structures on the bi-smash product Hopf algebra.
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This is the first part of a paper that classifies 2-compact groups. In this first part we formulate a general classification scheme for 2-compact groups in terms of their maximal torus normalizer pairs. We apply this general classification procedure to the simple 2-compact groups of the A-family and show that any simple 2-compact group that is locally isomorphic to PGL(n+1,ℂ) is uniquely N-determined. Thus there are no other 2-compact groups in the A-family than the ones we already know....