Let k be a field. Let also (F, G) be a matched pair of groups. We give necessary and sufficient conditions on a pair (\sigma, \tau) of 2-cocycles in order that the crossed product algebra and the crossed coproduct coalgebra k^G{ }^{ \tau}#_{ \sigma} kF combine into a braided Hopf algebra. We also discuss diagonal realizations of such braided Hopf algebras in the category of Yetter-Drinfeld modules over a finite group.
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