dadli,
Вариант...
<!DOCTYPE html>
<html>
<head>
<title></title>
<script type="text/javascript">
function ISchecked(name)
{
var elements = document.getElementsByName(name);
for (var i=0; i<elements.length; i++) {
if (elements[i].checked) return true
}
return false
}
</script>
</head>
<body>
<input type="radio" name="imia" value="Alex"> Alex
<br>
<input type="radio" name="imia" value="John"> John
<br>
<input type="radio" name="imia" value="Billy"> Billy
<br>
<input type="button" value="go" onclick="alert(ISchecked('imia'));">
</body>
</html>