"For example, it may serve one group A to create the apparancy that two other groups B and C should hate each other, because that allows the original group A to avoid attention.

I am inclined toward the latter explanation, except that I can't quite identify group A. ;>)

Dwight D Eisenhower, in his farewell address at the end of his two-term Presidency, coined a phrase to name "group A" way back when it was just beginnning to form up and solidify its economic and political power: the Military-Industrial Complex.