Solution Found!
Prove that An is normal in Sn.
Chapter 9, Problem 2E(choose chapter or problem)
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,