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Abstract
Primitive prime divisors play an important role in group theory and number theory. We study a certain numbertheoretic quantity, called φ∗_{n}(q), which is closely related to the cyclotomic polynomial φ_{n} (x) and to primitive prime divisors of q^{n}  1. Our definition of φ∗_{n}(q) is novel, and we prove it is equivalent to the definition given by Hering. Given positive constants c and k, we provide an algorithm for determining all pairs (n; q) with φ∗_{n}(q) ≤ cn^{k}. This algorithm is used to extend (and correct) a result of Hering and is useful for classifying certain families of subgroups of finite linear groups.
Original language  English 

Pages (fromto)  122135 
Number of pages  14 
Journal  Journal of the Australian Mathematical Society 
Volume  102 
Issue number  1 
DOIs  
Publication status  Published  1 Feb 2017 
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Dive into the research topics of 'Primitive prime divisors and the nTH cyclotomic polynomial'. Together they form a unique fingerprint.Projects
 1 Finished

Finite linearly representable geometries and symmetry
Praeger, C., Glasby, S. & Niemeyer, A.
ARC Australian Research Council
1/01/14 → 31/05/19
Project: Research