Write the following permutations as the product of disjoint cycle.

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written 5.3 years ago by

teamques10 ★ 64k

I. Given f= (1,3,2,5) (1,4,5) (2,5,1)

= (1,3,2,5) (1,4,5) (2)

= (1,3,2,5) (2)

f(1)= 5

= (1,3,2,5) (1,4,5) (5)

= (1,3,2,5) (1)

f(2)= 3

= (1,3,2,5) (1,4,5) (3)

= (1,3,2,5) (3)

f(3)= 2

= (1,3,2,5) (1,4,5) (4)

= (1,3,2,5) (5)

f(4)= 1

5.f(5)= (1,3,2,5) (1,4,5) (2,5,1) (5)

= (1,3,2,5) (1,4,5) (1)

= (1,3,2,5) (4)

f(5)= 4

enter image description here

Hence, expressing permutation f as the product of disjoint cycle, we have

$\therefore$ f = (1,5,4) (2,3)

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