def METHOD_NAME(n):
    """
    Generates the alternating group on ``n`` elements as a permutation group.
    For ``n > 2``, the generators taken are ``(0 1 2), (0 1 2 ... n-1)`` for
    ``n`` odd
    and ``(0 1 2), (1 2 ... n-1)`` for ``n`` even (See [1], p.31, ex.6.9.).
    After the group is generated, some of its basic properties are set.
    The cases ``n = 1, 2`` are handled separately.
    Examples
    ========
    >>> G = AlternatingGroup(4)
    >>> G.is_group
    True
    >>> a = list(G.generate_dimino())
    >>> len(a)
    12
    >>> all(perm.is_even for perm in a)
    True
    See Also
    ========
    SymmetricGroup, CyclicGroup, DihedralGroup
    References
    ==========
    [1] Armstrong, M. "Groups and Symmetry"
    """
    # small cases are special
    if n in (1, 2):
        return PermutationGroup([Permutation([0])])
    a = list(range(n))
    a[0], a[1], a[2] = a[1], a[2], a[0]
    gen1 = a
    if n % 2:
        a = list(range(1, n))
        a.append(0)
        gen2 = a
    else:
        a = list(range(2, n))
        a.append(1)
        a.insert(0, 0)
        gen2 = a
    gens = [gen1, gen2]
    if gen1 == gen2:
        gens = gens[:1]
    G = PermutationGroup([_af_new(a) for a in gens], dups=False)
    if n < 4:
        G._is_abelian = True
        G._is_nilpotent = True
    else:
        G._is_abelian = False
        G._is_nilpotent = False
    if n < 5:
        G._is_solvable = True
    else:
        G._is_solvable = False
    G._degree = n
    G._is_transitive = True
    G._is_alt = True
    return G