# Permutation/8/25371486/45286713/Produkt/Fehlstände/Vorzeichenberechnung/Aufgabe

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Betrachte die beiden Permutationen

 ${\displaystyle {}x}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$ ${\displaystyle {}7}$ ${\displaystyle {}8}$ ${\displaystyle {}\sigma (x)}$ ${\displaystyle {}2}$ ${\displaystyle {}5}$ ${\displaystyle {}3}$ ${\displaystyle {}7}$ ${\displaystyle {}1}$ ${\displaystyle {}4}$ ${\displaystyle {}8}$ ${\displaystyle {}6}$
und
 ${\displaystyle {}x}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$ ${\displaystyle {}7}$ ${\displaystyle {}8}$ ${\displaystyle {}\tau (x)}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}2}$ ${\displaystyle {}8}$ ${\displaystyle {}6}$ ${\displaystyle {}7}$ ${\displaystyle {}1}$ ${\displaystyle {}3}$

Berechne ${\displaystyle {}\sigma \tau }$ und ${\displaystyle {}\tau \sigma }$. Bestimme die Anzahl der Fehlstände und das Vorzeichen

von ${\displaystyle {}\tau }$. Man gebe die Zyklendarstellung von ${\displaystyle {}\sigma }$ und von ${\displaystyle {}\sigma ^{3}}$ an. Was ist die Ordnung von ${\displaystyle {}\sigma }$?