Let n ≥ 3 be an integer. Recall that by labeling the vertices of a regular n-gon with numbers, we may view Dn as a subgr

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Let n ≥ 3 be an integer. Recall that by labeling the vertices of
a regular n-gon with numbers, we may view Dn as a
subgroup of Sn.
1. For which values of n is Dn isomorphic to
Sn? For those values of n where Dn ̸≈
Sn give an element from Sn that is
not in Dn.
2. Viewing Dn as a subgroup of Sn,
describe geometrically what the even and odd permutations of
Dn are, if any exist.
3. Is Dn sometimes/always/never a subgroup of
An? Justify.