Express as the product of disjoint cycle the permutation a) θ(1)=4 θ(2)=6 θ(1)=5 θ(4)=1 θ(5)=3 θ(6)=2 b) (1 6 3)(1 3 5 7)(6 7)(1 2 3 4 5) c) (1 2 3 4 5)(6 7)(1 3 5 7) Find the order of each of them help!


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Question Number 192339 by Mastermind last updated on 15/May/23

$Express as the product of disjoint$ $cycle the permutation$ $a) θ (1) = 4 θ (2) = 6 θ (1) = 5 θ (4) = 1$ $θ (5) = 3 θ (6) = 2$ $b) (1 6 3) (1 3 5 7) (6 7) (1 2 3 4 5)$ $c) (1 2 3 4 5) (6 7) (1 3 5 7)$ $Find the order of each of them$ $help!$
	Answered by aleks041103 last updated on 15/May/23

	$a)$ $θ = (\begin{matrix} 1 2 3 4 5 6 \\ 4 6 5 1 3 2 \end{matrix}) = (1 4) (2 6) (3 5)$ $b) (1 6 3) (1 3 5 7) (6 7) (1 2 3 4 5) =$ $= (\begin{matrix} 1 2 3 4 5 6 7 \\ 2 5 4 7 1 6 3 \end{matrix}) = (1 2 5) (3 4 7)$ $c) (1 2 3 4 5) (6 7) (1 3 5 7) =$ $= (\begin{matrix} 1 2 3 4 5 6 7 \\ 4 3 1 5 6 7 2 \end{matrix}) = (1 4 5 6 7 2 3)$ $a) ∣ θ ∣= l c m (2, 2, 2) = 2$ $b) ∣ (1 6 3) (1 3 5 7) (6 7) (1 2 3 4 5) ∣= l c m (3, 3) = 3$ $c) ∣ (1 2 3 4 5) (6 7) (1 3 5 7) ∣= l c m (7) = 7$
	Commented by Mastermind last updated on 18/May/23

	$Thank you so much sir$
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