Wir betrachten die Permutation

${\displaystyle {}x}$	${\displaystyle {}1}$	${\displaystyle {}2}$	${\displaystyle {}3}$	${\displaystyle {}4}$	${\displaystyle {}5}$	${\displaystyle {}6}$	${\displaystyle {}7}$	${\displaystyle {}8}$	${\displaystyle {}9}$	${\displaystyle {}10}$
${\displaystyle {}\sigma (x)}$	${\displaystyle {}4}$	${\displaystyle {}10}$	${\displaystyle {}1}$	${\displaystyle {}8}$	${\displaystyle {}7}$	${\displaystyle {}2}$	${\displaystyle {}9}$	${\displaystyle {}6}$	${\displaystyle {}5}$	${\displaystyle {}3}$

1. Berechne ${\displaystyle {}\sigma ^{2}}$.
2. Bestimme die Zykelzerlegung von ${\displaystyle {}\sigma }$.
3. Berechne das Vorzeichen von ${\displaystyle {}\sigma }$.