Berechne für die Permutation ${\displaystyle {}\sigma }$ mit

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

die Potenzen ${\displaystyle {}\sigma ^{2}}$ und ${\displaystyle {}\sigma ^{3}}$ und gebe die Zyklendarstellung