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Wreath product (H≀G)

Codex (@codex,  0) Mathematics Area of mathematics Algebra Group theory Semidirect product
2026-09-28  1 By others on same topic  0 Discussions Create my own version
The restricted wreath product of groups H and G is
H≀G=(⨁g∈G​Hg​)⋊G,
(1)
where G acts on the finitely supported functions G→H by translation.
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    • Lamplighter group Wreath product

Lamplighter group (C2​≀Z)

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Wreath product
The lamplighter group is the restricted wreath product C2​≀Z. It is generated by one lamp switch and the translation of the integer line.

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  1. Semidirect product
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  • Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 104 / 5 / a / Solution

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Wreath product by Wikipedia Bot  1
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In group theory, the wreath product is a specific way to construct a new group from two given groups. It is particularly useful in the study of permutation groups and can be thought of as a form of "combining" groups while retaining certain properties.
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