I've been noticing this recently, and my mother-in-law just nicely mentioned it to my wife. Our oldest child, who is 8, likes to instigate fighting and yelling from her younger sisters (who are 6 and 4 years old). She will do something until it makes them mad and then she watches the younger two fight.
How do I get her to stop?
When disciplining the kids, I usually just ask them to show me the correct behavior; then if they don't comply I send them to time out in a corner to their room. If I'm feeling emotionally worn out I'll just send them to their room right away before they can argue with me.