def METHOD_NAME(x):
    """
    Return true if x is an abelian group element, i.e., an element of
    type AbelianGroupElement.
    EXAMPLES: Though the integer 3 is in the integers, and the integers
    have an abelian group structure, 3 is not an AbelianGroupElement::
        sage: from sage.groups.abelian_gps.abelian_group_element import is_AbelianGroupElement
        sage: is_AbelianGroupElement(3)
        False
        sage: F = AbelianGroup(5, [3,4,5,8,7], 'abcde')
        sage: is_AbelianGroupElement(F.0)
        True
    """
    return isinstance(x, AbelianGroupElement)