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.

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  • 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. An important distinction between the wreath product of groups A and H, and other products such as the direct sum, is that the actual product is a semidirect product of multiple copies of A by H, where H acts to permute the copies of A among themselves.
  • Das Kranzprodukt ist ein Begriff aus der Gruppentheorie und bezeichnet ein spezielles semidirektes Produkt von Gruppen.
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  • 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.
  • Das Kranzprodukt ist ein Begriff aus der Gruppentheorie und bezeichnet ein spezielles semidirektes Produkt von Gruppen.
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  • Wreath product
  • Kranzprodukt
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