Javacript Group generators

function generators ( group, operation, groupMod) {
    
    var generatorList = [];

    for ( var element in group ) {
    
        var elementCycle = [];
        
        for (var i = 1; i <= groupMod; i++) {
         
            if (operation == 'mult') {
                elementCycle.push(Math.pow(element, i));
            } else {
                elementCycle.push((element * i));
            }
            
            for (var i = 0; i < elementCycle.length; i++) {
                   elementCycle[i] = elementCycle[i] % groupMod;
            }
            
            elementCycle.sort();
            var validComparison = true;
            for (var i = 0; i < group.length; i++) {
            
                if ( group[i] !== elementCycle[i] ) {
                  validComparison = false;   
                }
                
            }
            
            if (validComparison) 
                generatorList.push(element);
            
        }
    }

    return generatorList;

}

// generators([1,3,5,7,9,13,15,17,19,21], 'mult', 22);