High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, the wreath product of group theory is a specialized product of two groups, based on a semidirect product. Wreath products are an important tool in the classification of permutation groups and also provide a way of constructing interesting examples of groups. The standard or unrestricted wreath product of a group A by a group H is written as A wr H, or also A H. In addition, a more general version of the product can be defined for a group A and a transitive permutation group H acting on a set U, written as A wr (H, U). By Cayley's theorem, every group H is a transitive permutation group when acting on itself; therefore, the former case is a particular example of the latter.

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