When there is no external torque acting on a system the quantity which has a necessarily zero magnitude is 

Torque is defined as the rate of change of angular momentum. So, if torque is zero, the rate of change of angular momentum will be zero. An important thing to note is that one may think how kinetic energy can change if torque is zero. For this, consider the example of a ballet dancer, when she/he pulls in her hands while rotating she/he becomes faster but angular momentum remains constant since net torque is zero. But her kinetic energy  increases.