Canonical Actions of Wreath Products
If the group A acts on a set Λ then there are two canonical ways to construct sets from Ω and Λ on which A WrΩ H (and therefore also A wrΩ H) can act.
- The imprimitive wreath product action on Λ×Ω.
- If ((aω),h)∈A WrΩ H and (λ,ω')∈Λ×Ω, then
-
- .
- The primitive wreath product action on ΛΩ.
- An element in ΛΩ is a sequence (λω) indexed by the H-set Ω. Given an element ((aω), h) ∈ A WrΩ H its operation on (λω)∈ΛΩ is given by
-
- .
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