def METHOD_NAME(n, base_ring, invfac=None):
    """
    Abelian group on `n` generators which represents a homology group in a
    fixed degree.
    INPUT:
    - ``n`` -- integer; the number of generators
    - ``base_ring`` -- ring; the base ring over which the homology is computed
    - ``inv_fac`` -- list of integers; the invariant factors -- ignored
      if the base ring is a field
    OUTPUT:
    A class that can represent the homology group in a fixed
    homological degree.
    EXAMPLES::
        sage: from sage.homology.homology_group import HomologyGroup
        sage: G = AbelianGroup(5, [5,5,7,8,9]); G                                       # needs sage.groups
        Multiplicative Abelian group isomorphic to C5 x C5 x C7 x C8 x C9
        sage: H = HomologyGroup(5, ZZ, [5,5,7,8,9]); H
        C5 x C5 x C7 x C8 x C9
        sage: AbelianGroup(4)                                                           # needs sage.groups
        Multiplicative Abelian group isomorphic to Z x Z x Z x Z
        sage: HomologyGroup(4, ZZ)
        Z x Z x Z x Z
        sage: # needs sage.libs.flint (otherwise timeout)
        sage: HomologyGroup(100, ZZ)
        Z^100
    """
    if base_ring.is_field():
        return VectorSpace(base_ring, n)
    # copied from AbelianGroup:
    if invfac is None:
        if isinstance(n, (list, tuple)):
            invfac = n
            n = len(n)
        else:
            invfac = []
    if len(invfac) < n:
        invfac = [0] * (n - len(invfac)) + invfac
    elif len(invfac) > n:
        raise ValueError("invfac (={}) must have length n (={})".format(invfac, n))
    return HomologyGroup_class(n, invfac)