Primitive prime divisors and the nTH cyclotomic polynomial

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    Abstract

    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 φn (x) and to primitive prime divisors of qn - 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) ≤ cnk. 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
    Volume102
    Issue number1
    DOIs
    Publication statusPublished - 1 Feb 2017

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