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 $p^{k}$, where $p$ is prime, and $k$ a nonnegative integer, the prime-base logarithm of order is $k$.

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