ActionScript3 :: Flex : Programmatically Associate A RadioButton With A RadioButtonGroup?

I have a UI component that, for various reasons, I have to construct programatically. The component is a table of radio buttons grouped by column.Right now, I'm constructing the column groups like so:

private function createGroupsForItemList(items: XMLList): void {
for each (var item: XML in items) {
var rbGroup: RadioButtonGroup = new RadioButtonGroup();
groups[item.@level.toString()] = rbGroup;
}
}

I'm trying to associate the RadioButton instances with the column groups like so:

private function createValueControl(item: XML): UIComponent {
var control: RadioButton = new RadioButton();
control.label = "";

[code]...

I can see in the debugger that the control has an association to the group:

control.group == groups[item.@level.toString()]

However, I can see equally that the group does not know anything about the control:

group.radioButtons.length == 0

I imagine that this is because the setter for group in RadioButton is a dumb setter; all it does is copy to the variable, which doesn't do the magic that groupName does. However, I can't seem to find the value I should use to set the RadioButton.groupName property correctly.So, in short, I'm stumped on how to get these bits to talk to each other. How do I do this?

-- EDIT -- It turns out that I can have the groups created and associated simply by setting the groupName property, but I can't get at the group to set up a selection listener; the group is NULL immediately after the setting process, which means that the second line below throws the Flex equivalent of an NPE:

control.groupName = groupNameForLevel(item);
control.group.addEventListener(Event.SELECT, updateSelection);