Concept

Wreath product

Summary
In group theory, the wreath product is a special combination of two groups based on the semidirect product. It is formed by the action of one group on many copies of another group, somewhat analogous to exponentiation. Wreath products are used in the classification of permutation groups and also provide a way of constructing interesting examples of groups. Given two groups A and H (sometimes known as the bottom and top), there exist two variations of the wreath product: the unrestricted wreath product A \text{ Wr } H and the restricted wreath product A \text{ wr } H. The general form, denoted by A \text{ Wr}{\Omega} H or A \text{ wr}{\Omega} H respectively, requires that H acts on some set \Omega; when unspecified, usually \Omega = H (a regular wreath product), though a different \Omega is sometimes implied. The two variations coincide when A
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