Radio buttons group XAML
You have to specify a GroupName for the element.
<RadioButton GroupName="Group1"/>
BitKFu's suggestion of using the GroupName property will work, but there is a caveat. If you use group names, the scope for RadioButton groups becomes different.
If you create a UserControl with 3 RadioButtons all with a GroupName of "MyRadioGroup" and place 2 such controls in your Window, you will notice that all 6 RadioButtons act like they are one group.
This happens because when the RadioButton is updating other RadioButtons it normally only adjusts RadioButtons that are children of its immediate parent DependencyObject. However, when the GroupName is used the scope expands to the root Visual (Window, for example) and it will adjust all RadioButtons under that root that have the same GroupName.
So sometimes it's better to just separate them with an extra panel.