splitting array elements in javascript split function

You need to add to array2 and use both elements from the returned array that String.prototype.split returns - i.e. 0 is the left hand side and 1 is the right hand side of the dot.

var array = ["a.READ", "b.CREATE"]
var array1 = []; // better to define using [] instead of new Array();
var array2 = [];

for (var i = 0; i < array.length; i++) {
    var split = array[i].split(".");  // just split once
    array1.push(split[0]); // before the dot
    array2.push(split[1]); // after the dot
}
console.log("array1", array1);
console.log("array2", array2);

We'll start off with a generic transpose function for two-dimensional arrays:

function transpose(arr1) {               // to transpose a 2d array
    return arr1[0].map(                  // take the first sub-array and map
        function(_, i) {                 // each element into
            return arr1.map(             // an array which maps
                function(col) {          // each subarray into
                    return col[i];       // the corresponding elt value
                }
            );
        }
    );
}

Now the solution is just

transpose(                        // transpose the two-dimensional array
    array.map(                    // created by taking the array and mapping
        function(e) {             // each element "a.READ" into
            return e.split('.');  // an array created by splitting it on '.'
        }
    )
)

You are adding nothing to array2. Please use indexes properly , like below:

var array1=new Array();
var array2 = new Array();

for (var i = 0; i < array .length; i++) {
  array1.push(array [i].split(".")[0]);
  array2.push(array [i].split(".")[1]);
}

you can do something like this

var array =["a.READ","b.CREATE"];
var arr1= [], arr2= [];

array.forEach(function(item,index,arr){
  item.split('.').forEach(function(item,index,arr){
    if(index % 2 === 0){
      arr1.push(item);
    }else{
      arr2.push(item);
    }
  });      
});

console.log(arr1);
console.log(arr2);

DEMO

I guess this is a bit redundant but, the split method actually returns and array. Although your code was off you were not modifying array2. Consider the following.

var array = [ "a.READ" , "b.CREATE" ]
  , array1 = []
  , array2 = []
  // cache array length
  , len = array.length;

for ( var i = 0; i < len; i++ ) {
    // the split method returns a new array
    // so we will cache the array
    // push element 0 to array1
    // push element 1 to array2
    var newArr = array[ i ].split('.');
    array1.push( newArr[ 0 ] );
    array2.push( newArr[ 1 ] );
}

console.log( 'array1: ', array1 );
console.log( 'array2: ', array2 );

Use this:

for (var i = 0; i < array .length; i++) {
  var parts = array[i].split('.');
  array1.push(parts[0]);
  array2.push(parts[1]);
}

You have not assigned any value to Array2. You can do as shown below.

var array1=[];
var array2 = [];

for (var i = 0; i < array .length; i++) {
    var arrayTemp=[];
    arrayTemp.push(array [i].split("."));
    array1.push(arrayTemp[0]);          
    array2.push(arrayTemp[1]);
}