var obj={a:{b:'c'}},
key='a.b.c',
get_object_property_by_key=function(object,key){
if(typeof object!='object')
return object;
key=key.split('.');
for(var i=0;i<key.length;i++){
if(!object[key[i]])
return object;
else
object=object[key[i]];
};
return object;
};
alert(get_object_property_by_key(obj,key));