Difference between revisions of "Prime-base logarithm of order"

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(Created page with '==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 grou…')
 
 
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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 <math>p^k</math>, where <math>p</math> is prime, and <math>k</math> a nonnegative integer, the prime-base logarithm of order is <math>k</math>.
 
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 <math>p^k</math>, where <math>p</math> is prime, and <math>k</math> a nonnegative integer, the prime-base logarithm of order is <math>k</math>.
  
The number <math>k</math> is sometimes a more useful size measure than <math>p^k</math>.
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The number <math>k</math> is sometimes a more useful size measure than <math>p^k</math>. It also permits more ready comparison with such measures as the [[nilpotency class]], [[derived length]], and [[Frattini length]].

Latest revision as of 02:34, 26 March 2010

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.