Question

What is the number of even permutation in S3?​

Answer 1

Answer:

An even permutation is a permutation obtainable from an even number of two-element swaps, i.e., a permutation with permutation symbol equal to .

Answer 2

Tip:

• A permutation that can be expressed as a product of an even number of 2-cycles , is called an even permutation.

Explanation:

• We have given $S_3$.

• We have to find the number of even permutation.

Step

Step 1 of 2:

$S_3=\left[\begin{array}{ccc}1&2&3\\1&2&3\end{array}\right]$

$S_3$ has elements $\{1,(1~2),(1~3),(2~3),(1~2~3),(1~3~2)\}$

Order of $S_3$ is $3!=6$

Number of elements of order $2=3$

Number of elements of order $3=2$

Step 2 of 2:

We know that even permutation can be expressed as a product of 2-cycles.

So, $S_3$ has 3 even permutation.

Final Answer: