# Prime-base logarithm of order

## Definition

For a group of prime power order, the **prime-base logarithm of order** is the logarithm of its order to base equal to the prime. In other words, for a group of order , where is prime, and a nonnegative integer, the prime-base logarithm of order is .

The number is sometimes a more useful size measure than . It also permits more ready comparison with such measures as the nilpotency class, derived length, and Frattini length.