- Glasby S
- Lübeck F
- Niemeyer A
- et al.

Journal of the Australian Mathematical Society (2017) 102(1) 122-135

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3Readers

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.

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APA

Glasby, S. P., Lübeck, F., Niemeyer, A. C., & Praeger, C. E. (2017). Primitive prime divisors and the nTH cyclotomic polynomial. *Journal of the Australian Mathematical Society*, *102*(1), 122–135. https://doi.org/10.1017/S1446788715000269

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