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.
Given two groups A and H there exist two variations of the wreath product: the unrestricted wreath product A Wr H (also written A≀H) and the restricted wreath product A wr H. Given a set Ω with an H-action there exists a generalisation of the wreath product which is denoted by A WrΩ H or A wrΩ H respectively.
Read more about Wreath Product: Definition, Notation and Conventions, Properties, Canonical Actions of Wreath Products, Examples
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