Prime-base logarithm of order

From Groupprops
Jump to: navigation, search

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.