Greetings Jennifer,
If I remember correctly, the Authorization Group for Equipments can only be used effectively if it is combined with a non-blank value in the Equipment master data. In other words, the Authorization Group prohibits anybody without the relevant I_BEGRP value from displaying or changing the Equipment - and if the value is left blank, then there is nothing to base this restriction on.
As Jogeswara Rao Kavalasaid, I believe there are no shortcuts here - you'd need to have a role that would allow the display of Equipments with I_BEGRP = 'Y' to assign to all users, then a role with I_BEGRP = 'X' to some users only, and then each and every Equipment would have to have a non-blank value of either X or Y to the Authorization group.
This could necessitate configuring the Authorization Group screen field as mandatory for IE01/IE02 t-codes and also maintenance for the value for existing Equipments, e.g. via IBIP.