..

Here is compilable code..

<sscce>
import java.awt.*;
import java.awt.event.*;
import javax.swing.*;
import java.util.*;

public class ArrowKeyNavigation {

 public static void main(String[] args) {
   JFrame f = new JFrame("ButtonGroupNavigation");
   f.setDefaultCloseOperation(JFrame.DISPOSE_ON_CLOSE);

   /* from
http://java.sun.com/docs/books/tutorial/uiswing/misc/focus.html
   */
   Set forwardKeys = f.getFocusTraversalKeys(
     KeyboardFocusManager.FORWARD_TRAVERSAL_KEYS);
   Set newForwardKeys = new HashSet(forwardKeys);
   newForwardKeys.add(
     KeyStroke.getKeyStroke(KeyEvent.VK_RIGHT, 0));
   f.setFocusTraversalKeys(
     KeyboardFocusManager.FORWARD_TRAVERSAL_KEYS,
       newForwardKeys);

   Set backwardKeys = f.getFocusTraversalKeys(
     KeyboardFocusManager.BACKWARD_TRAVERSAL_KEYS);
   Set newBackwardKeys = new HashSet(backwardKeys);
   newBackwardKeys.add(
     KeyStroke.getKeyStroke(KeyEvent.VK_LEFT, 0));
   f.setFocusTraversalKeys(
     KeyboardFocusManager.BACKWARD_TRAVERSAL_KEYS,
       newBackwardKeys);

   Container c = f.getContentPane();
   c.setLayout(new GridLayout(1,0));

   ButtonGroup bg = new ButtonGroup();
   for (int ii=0; ii<4; ii++) {
     JRadioButton b = new JRadioButton("Btn " + ii);
     bg.add( b );
     c.add( b );
   }

   f.pack();
   f.setVisible(true);
 }
}
</sscce>

HTH

Andrew T.