include 'db.php';
function addGroup($group_name){

$stmt=$pdo->prepare('INSERT INTO group_back SET name_group=? ');
$stmt=$pdo->execute(array($group_name));

}

Undefined variable:pdo

$host = '*****';
$db   = '*****';
$user = '*****';
$pass = '*****';
$charset = 'utf8';

$dsn = "mysql:host=$host;dbname=$db;charset=$charset";
$opt = [
    PDO::ATTR_ERRMODE            => PDO::ERRMODE_EXCEPTION,
    PDO::ATTR_DEFAULT_FETCH_MODE => PDO::FETCH_ASSOC,
    PDO::ATTR_EMULATE_PREPARES   => false,
];
$pdo = new PDO($dsn, $user, $pass, $opt);