### 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 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 |
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Pages (from-to) | 122-135 |

Number of pages | 14 |

Journal | Journal of the Australian Mathematical Society |

Volume | 102 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2017 |

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### Cite this

*Journal of the Australian Mathematical Society*,

*102*(1), 122-135. https://doi.org/10.1017/S1446788715000269