## 🎨 Visuaalne seletus: Wreath Product

Kujutame ette järgmist olukorda:

- Sul on **rühm $A$**, mis esindab näiteks **tulesid**, mida saab sisse või välja lülitada (nt $\mathbb{Z}_2$).
- Sul on **rühm $B$**, mis esindab **lülitite paigutust** (nt $\mathbb{Z}_3$, kolme positsiooniga).

Wreath product $A \wr B$ tähendab, et:

- Iga **positsioon** $b \in B$ saab oma **valguse** $a_b \in A$,
- Rühm $B$ saab **nihutada** neid positsioone, muutes, milline tuli on kus.

See on nagu **valguspaneel**, kus iga tuli on seotud kindla kohaga, aga keegi saab kogu paneeli pöörata või ümber paigutada.

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## 🧮 Praktiline näide: $\mathbb{Z}_2 \wr \mathbb{Z}_3$

- $\mathbb{Z}_2 = {0, 1}$: iga tuli on kas **väljas $(0)$** või **sees $(1)$**.
- $\mathbb{Z}_3 = {0, 1, 2}$: kolm positsiooni.

Element $(f, b)$ wreath productis tähendab:

- Funktsioon $f: \mathbb{Z}_3 \to \mathbb{Z}_2$, nt $f = (1, 0, 1)$ — tuled 0 ja 2 on sees.
- Element $b = 1 \in \mathbb{Z}_3$ — nihutame positsioone ühe võrra edasi.

Siin on skeem, mis illustreerib **wreath product'i** $\mathbb{Z}_2 \wr \mathbb{Z}_3$ toimimist:

![Wreath product Z2 wr Z3 diagramm](data:image/png;base64,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)

### Selgitus:

- **Vasakul**: algne seisund, kus iga positsioonil $(0, 1, 2)$ on oma tuli (kollane = sees, hall = väljas).
    - Funktsioon $f = [1, 0, 1]$: positsioonid 0 ja 2 on sees.
- **Paremal**: pärast $\mathbb{Z}_3$ tegevust — **nihutame kõik positsioonid ühe võrra edasi**.
    - Tulemuseks on uus funktsioon $f' = [1, 1, 0]$, kuna tuled nihkuvad.

Sinised nooled näitavad, kuidas tuled liiguvad positsioonide vahel.

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Kas soovid ka **teoreetilist üldistust** või **teise näite** mõne muu rühmaga?