Question

if o = (13 4) (25) then order of g is​

Answer 1

Answer:

2x+3;x;9−3x

2x+3;x;3x−9

x;2x+3;3x−9

2(x+3);x;9−3x

Answer 2

The order of g = 6

Given :

g = (1 3 4)(2 5)

To find :

The order of g

Solution :

Step 1 of 3 :

Write down the given permutation

Here the given permutation is

g = (1 3 4)(2 5)

Step 2 of 3 :

Check the permutation commute or not

(1 3 4) and (2 5) are disjoint

So the permutation commute

Step 3 of 3 :

Find the order

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

We know that if a and b are elements of a group such that o(a) = m , o(b) = n and gcd(m, n) = 1 then o(ab) = mn

Using this result we get

The order of g

= Order of (1 3 4)(2 5)

= o(1 3 4) × o(2 5)

= 3 × 2

= 6

Correct question : If g = (1 3 4)(2 5) then order of g is

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