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.