IteratedWreathProduct — Mathlib

English

The nth iterated wreath product G is defined recursively by IteratedWreathProduct G 0 = PUnit and IteratedWreathProduct G (n+1) = (IteratedWreathProduct G n) ≀ᵣ G.

Русский

Н-й повторенный вентовый произведение G определяется рекурсивно: IteratedWreathProduct G 0 = PUnit и IteratedWreathProduct G (n+1) = IteratedWreathProduct G n ≀ᵣ G.

LaTeX

$$$ IteratedWreathProduct(G,n) = \begin{cases} PUnit, & n=0 \\ IteratedWreathProduct(G,n) \wr_{\mathrm{r}} G, & n>0 \end{cases} $$$

Lean4

/-- The wreath product of group `G` iterated `n` times. -/
def IteratedWreathProduct (G : Type u) : (n : ℕ) → Type u
  | 0 => PUnit
  | n + 1 => (IteratedWreathProduct G n) ≀ᵣ G

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