Why not?

I think the problem that you are having is that you use currentThread().getGroup() inside the setPriorities() method. This is referring to the only thread that is running, which I call the main thread (.start() isn't called on any of the thread objects created in main). Add this to the code inside .setPriorities() method and you can see what I mean:

public synchronized void setPriorities() {
    int MAX = MAX_PRIORITY;
    ThreadGroup group = currentThread().getThreadGroup();
    System.out.println(group);  //<--- this line
    //...
}

To refer to the thread object that the .setPriorities() method belongs to you would use 'this'; as in this.getThreadGroup(). Now, with all that being said, you are over complicating this task. When a ThreadGroup has a max priority set then the .setPriority() method will automatically set it to that number if a higher number is passed to it. Take this code for example:

ThreadGroup group = new ThreadGroup("someName");
group.setMaxPriority(7);

Thread x = new MyThread(group, "name");
x.setPriority(10);
System.out.println("The Priority of thread x is: " + x.getPriority());

This code creates a group with a max priority of 7. Then it creates a thread as part of this group and uses its setPriority() to set it to 10. Then it outputs the priority of the thread and the output shows that it is only 7. You should be able to reduce the code inside the .setPriorities() method by quite a bit without having to figure out if MAX_PRIORITY or .group.getMaxPriority() is the number you need to use.