How to relate nodes in Drupal 7
The best way is to use the Entity Reference Module.


Install the module
At the Product add a field My Product Group and Field Type: Entity Reference. If you have many Products use the autocomplete widget.
On the next page chose Target type: Node and then the as Target bundles the Product Group.


Now when you add a ‘Product’ you can assign the parent ‘Product Group’.

Do the same for Application and Product.

The final structure will be:

- Product Group
- (have) Product
-- (have) Application


To display the results is another story. You can go to ‘Manage display’ of the content type and Render the entity. Or you can use views if you like something more complex.