Question

Which of the following statements are correct:
A. Permutation group $S_n$ has order $n!$, $n > 1$.
B. Alternating group $A_n$ of degree $n$ has order $\frac{n!}{2}$, $n > 1$. C. Set of all even permutations forms a subgroup of $S_n$.
D. Every permutation in $S_n$, $n > 1$ is a product of 2-cycles.
E. $A_4$ has a subgroup of order 6.
Choose the correct answer from the options given below:

• A. A, B, C, D Only
• B. B, C, D, E Only
• C. A, B, C Only
• D. A, B, D Only

Hint:

Remember that $A_4$ (order 12) is the classical example showing that the converse of Lagrange's theorem does not hold, as it has no subgroup of order 6.

Answer 1

The Correct Option is A