Problem with Jump Action C#

Hello, I'm making a plat-former game Mario style and i want to limit the player to jump once when on ground, but with my current algorithms the player can jump unlimited times. My character (which the players control) script is:

 //floats that sets current speed, jump power, and max speed respectively
     public float speed = 50f;
     public float jumpPower = 150f;
     public float maxSpeed = 3f;
     //bool that sets if player is colliding with ground
     public bool onGround = true;
 
     private Rigidbody2D rg2d;
     private Animator anim;
 
     void Start ()
     {
         rg2d = gameObject.GetComponent<Rigidbody2D> ();
         anim = gameObject.GetComponent<Animator> ();
     }
 
     void Update () 
     {
         anim.SetFloat ("Speed",Math.Abs( Input.GetAxis ("Horizontal")));
         anim.SetBool ("On Ground", onGround);
 
         //flips the player animation according to his movement
         if (Input.GetAxis ("Horizontal") < -0.1f) 
         {
             transform.localScale = new Vector3 (-1, 1);
         }
         if (Input.GetAxis ("Horizontal") > 0.1f) 
         {
             transform.localScale = new Vector3 (1, 1);
         }
         //if the player isn't on ground and pressing JumpButton, player will jump
         if (Input.GetButtonDown ("Jump") && onGround)
         {
             rg2d.AddForce (Vector2.up * jumpPower);
         }
 
     }
 
     void FixedUpdate ()
     {
         float h = Input.GetAxis ("Horizontal");
 
         //moving player on X axis
         rg2d.AddForce ((Vector2.right * speed) * h);
 
         //limiting player movement on X axis
         if (rg2d.velocity.x > maxSpeed)
         {
             rg2d.velocity = new Vector2 (maxSpeed, rg2d.velocity.y);
         }
         if (rg2d.velocity.x < -maxSpeed)
         {
             rg2d.velocity = new Vector2 (-maxSpeed, rg2d.velocity.y);
         }
 
     }

and i putted right under the character a child gameObject named GroundCheck that will change onGround bool within certain conditions:

 void Start ()
     {
         player = gameObject.GetComponentInParent<Player> ();
     }
         //this GroundCheck script purpose is to change player.onGround bool according to certain conditions.
         //the bool onGround will be positive when GroundCheck is colliding with the ground and negative when not colliding with the ground.
     void OnTriggerEnter2D(Collider2D other)
     {
         player.onGround = true;
     }
 
     void onTriggerStay2D(Collider2D other)
     {
         player.onGround = true;
     }
     void onTriggerExit2D(Collider2D other)
     {
         player.onGround = false;
     }

But when i run the game, the player can jump unlimited times want and can fly out of the window. Could someone please notice the problem I have with the scripting and correct me?