Wreath Product

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 AH) 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

Famous quotes containing the words wreath and/or product:

    And before, with banner red,
    Through the blizzard snow unseen,
    All unharmed by hail of lead,
    With a step like snow so light,
    Showered in myriad pearls of snow.
    Crowned in wreath of roses white,
    Christ leads onward as they go.
    Alexander Blok (1880–1921)

    Whenever a taboo is broken, something good happens, something vitalizing.... Taboos after all are only hangovers, the product of diseased minds, you might say, of fearsome people who hadn’t the courage to live and who under the guise of morality and religion have imposed these things upon us.
    Henry Miller (1891–1980)