def get_log_file_name(file_path):
    """
    Save only the filename and the subdirectory it is in, strip off all prior
    paths.  If the file ends in .gz, remove that too.  Convert to lower case.
    """
    file_name = '/'.join(file_path.lower().split('/')[-1:])
    if len(file_name) > 3 and file_name[-3:] == ".gz":
        file_name = file_name[:-3]
    return file_name