Primitive prime divisors and the nTH cyclotomic polynomial

Stephen GLASBY, Frank Lubeck, Alice Niemeyer, Cheryl Praeger

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Primitive prime divisors play an important role in group theory and number theory. We study a certain number-theoretic 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 languageEnglish
Pages (from-to)122-135
Number of pages14
JournalJournal of the Australian Mathematical Society
Issue number1
Publication statusPublished - 2017


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