Creating a nested list using JSON and jquery

Hi Below is an example of my JSON, HTML and jquery code: Json:

{
"node":[
{"name":"XXX",
 "child":[ {"name":"acb"},
 {"name":"txy"}
 ]
},
{"name":"ZZZ",
 "child":[{"name":"ism"},
 {"name":"sss"}
 ]
},
{"name":"PPP"},
{"name":"QQQ"}
]
} 

      

        
        
        
      

    

JQuery code:

$(document).ready(function(){
            var $ul=$('<ul></ul>');
            $.getJSON('test1.json', function(json) {
                    $.each(json.node, function(key,value){
                            getList(value, $ul);
                                               })
                                            });
            $ul.appendTo("body");
                           });
                       function getList(item, $list) {

    if (item) {
        if (item.name) {
            $list.append($('<li><a href="#">' + item.name + '</a>' +"</li>"));
              }
        if (item.child && item.child.length) {
            var $sublist = $("<ul/>");
            $.each(item.child, function (key, value) {
                getList(value, $sublist);
            });
            $list.append($sublist);
        }
    }
}

      

        
        
        
      

    

So when I run this code the list is returned as

<ul>
<li></li>
<ul>
<li></li>
<li></li>
</ul>
</ul> .. and so on . But i don't want my list to be this was i need it like :

<ul>
<li>
<ul>
<li></li>
<li></li>
</ul>
</li>
<li>
<ul>
<li></li>
</ul>
</li>
</ul> 

      

        
        
        
      

    

Please give me how I can change my function to achieve a nested list in this way! .. Thanks in advance.