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Prove that An is normal in Sn.

Chapter 9, Problem 2E

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QUESTION:

Problem 2E

Prove that An is normal in Sn.

Questions & Answers

QUESTION:

Problem 2E

Prove that An is normal in Sn.

ANSWER:

Step 1 of 2

Let  and then,  is even and  is even or odd.

Here,  are transpositions.

If s is even then  

Inverse of product of transposition is just reverse order of transposition.

So,

Here, r and s are even so the sum (s + r + s) is also even.

Therefore,  

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