Abstract Algebra

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Moderate

Number of Even Permutations in a Group

ABSALG-1BDIQN

Let $H$ be a subgroup of $S_n$ for some $n$. Let $\alpha$ be the fraction of elements of $H$ that are even permutations.

What are the possible values of $\alpha$?

Select ALL that apply.

A

$0$

B

$\cfrac{1}{4}$

C

$\cfrac{1}{2}$

D

$\cfrac{3}{4}$

E

$1$