for m=3 you have to use some cubic polynomial whose determinant is a square in Q, so that the Galois group does not contain any odd permutations
for other cases, cyclotomic polynomial suffices
Seems like a slight typo there. It should be a "discriminant".
For a concrete example,
If , then the permutation is an element of if and only if it fixes the square root of the discriminant D.
We know that A_3 = Z_3. So the possible polynomial can be
and its discriminant is 49. Then, if the splitting field of f(x) is K, [K:Q]=3 and the order of Gal(K/Q) is 3.