Algebras mõiste **"wreath product"** (eesti keeles sageli "põimikkorrutis") tuleb peamiselt **rühmateooriast**, kuid seda kasutatakse ka **algebrailistes struktuurides** nagu poolrühmad, Lie-algebrad ja teised. See on viis kahe algebra või rühma kombineerimiseks viisil, mis säilitab teatud sümmeetria ja struktuuri.

### Wreath product rühmateoorias

Kui sul on kaks rühma $A$ ja $B$, siis nende **wreath product** $A \wr B$ on ligikaudu öeldes:

- **Pooldirektne korrutis** rühmade vahel, kus:
    - $A^B$ on funktsioonide hulk $B \to A$ (ehk iga $b \in B$ saab oma $A$-elemendi),
    - $B$ tegutseb selle funktsioonide hulga peal nihutades argumente.

Formaalne definitsioon: $(A \wr B) = A^B \rtimes B$

See tähendab, et:

- Iga element on kujul $(f, b)$, kus $f: B \to A$ ja $b \in B$,
- Korrutamine toimub reegli järgi: $(f_1, b_1)(f_2, b_2) = (f_1 \cdot (f_2 \circ b_1^{-1}), b_1 b_2)$

### Intuitsioon

Wreath product on kasulik näiteks **automaatide teoorias**, **kombinatoorikas** ja **grupi tegevustes**, kus üks rühm "kontrollib", kuidas teine rühm käitub või muutub.

### Näide

Kui võtame $A = \mathbb{Z}_2$ (kaheelemendiline tsükliline rühm) ja $B = \mathbb{Z}_3$, siis $\mathbb{Z}_2 \wr \mathbb{Z}_3$ on rühm, mis koosneb kolmest koopiafunktsioonist $\mathbb{Z}_3 \to \mathbb{Z}_2$ ja $\mathbb{Z}_3$ enda elementidest, mis määravad, kuidas neid funktsioone permuteeritakse.

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Kui soovid, võin tuua ka visuaalse skeemi või näite konkreetse algebra või rühma kohta. Kas sind huvitab rohkem **rakendus**, **visuaalne seletus**, või **seos mõne muu matemaatika valdkonnaga**?

Meie vestluses teemal **"Mis on algebras 'wreath product'"** käsitlesime järgmist:

- **Wreath product** (eesti keeles sageli "pärjatoode") on **matemaatiline konstruktsioon**, mida kasutatakse peamiselt **rühmateoorias**, kuid seda võib kohata ka **algebras ja teistes abstraktse algebra harudes**.
- See on **kombinatsioon kahest rühmast**: üks toimib teise rühma koopiate peal, mis on organiseeritud mingi indekseerimisstruktuuri (nt loenduvate elementide hulk) järgi.
- Wreath producti kasutatakse sageli **keerukamate rühmade konstrueerimiseks** väiksematest ja lihtsamatest rühmadest.
- Tüüpiline tähistus on näiteks $A \wr B$, kus $A$ on "baasrühm" ja $B$ on "toimiv rühm".
- Seda kasutatakse ka **automaatide teoorias**, **kooditeoorias**, ja **kombinatoorikas**, eriti kui on vaja kirjeldada **sümmeetriaid või korduvaid struktuure**.

Kui soovid, võin lisada ka näiteid või visuaalse skeemi, mis aitab paremini mõista, kuidas wreath product töötab. Kas soovid seda?

Vaatame üht lihtsat **näidet wreath productist rühmateoorias**, kasutades kahte hästi tuntud rühma:

### Näide: $\mathbb{Z}_2 \wr \mathbb{Z}_2$

Siin:

- $\mathbb{Z}_2$ on kaheelemendiline tsükliline rühm (sisaldab elemente 0 ja 1, liitmisega moodulis 2).
- Wreath product $\mathbb{Z}_2 \wr \mathbb{Z}_2$ tähendab, et meil on:
    - **baasrühm**: funktsioonid $f: \mathbb{Z}_2 \to \mathbb{Z}_2$, ehk kõik võimalikud määrangud kaheelemendilisele hulgale.
    - **toimiv rühm**: teine $\mathbb{Z}_2$, mis permuteerib baasrühma elementide asukohti.

### Samm-sammuline kirjeldus:

1. **Baasrühm** koosneb kõigist funktsioonidest $f: {0,1} \to \mathbb{Z}_2$. Neid on kokku $2^2 = 4$ (iga sisendi jaoks 2 valikut).
2. **Toimiv rühm** $\mathbb{Z}_2$ permuteerib neid kahte sisendit (0 ja 1), st kas jätab nad samaks või vahetab ära.
3. Wreath producti elemendid on kujul $(f, \sigma)$, kus $f$ on funktsioon ja $\sigma$ on permutatsioon.

### Kokkuvõttes:

Rühm $\mathbb{Z}_2 \wr \mathbb{Z}_2$ sisaldab 8 elementi ja on isomorfne **dihedraalse rühmaga $D_4$**, mis kirjeldab ruudu sümmeetriate hulka (pöörded ja peegeldused).

Kas soovid, et joonistan ka skeemi, mis näitab, kuidas see wreath product töötab visuaalselt?

Siin on skeem, mis illustreerib **wreath producti $\mathbb{Z}_2 \wr \mathbb{Z}_2$**:

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

### Selgitus skeemi kohta:

- **Sõlmed** tähistavad kõiki võimalikke funktsioone $f: {0,1} \to \mathbb{Z}_2$. Kokku on neid 4.
- **Nooled** tähistavad **toimiva rühma $\mathbb{Z}_2$** tegevust — antud juhul permutatsiooni, mis **vahetab sisendid 0 ja 1**.
- Kui näiteks funktsioon $f$ määrab $f(0) = 1$ ja $f(1) = 0$, siis permutatsiooniga "swap" saame uue funktsiooni, kus väärtused on vahetatud.

See skeem aitab visualiseerida, kuidas **wreath product** ühendab funktsioonid ja permutatsioonid üheks keerukamaks struktuuriks.

Kas soovid ka näidet mõne teise rühmaga, näiteks $\mathbb{Z}_2 \wr \mathbb{Z}_3$ või visuaali koos selgitava animatsiooniga?