If you have administration authorization for a field group that has been defined as relevant for authorizations by the system administrator, you can decide who has authorization for this field group.
For more information, see Status and Authorizations for Generic Objects.
By default, field groups inherit the authorizations of the object. For field groups for which you have administration authorization, you can overwrite this default.
Even if users have write authorization for a particular field group, they can only use this authorization if they have at least read authorization for the entire generic object.