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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