Primitive prime divisors and the nTH cyclotomic polynomial

Stephen GLASBY, Frank Lubeck, Alice Niemeyer, Cheryl Praeger

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Primitive prime divisors play an important role in group theory and number theory. We study a certain number-theoretic quantity, called f*n(q), which is closely related to the cyclotomic polynomial fn (x) and to primitive prime divisors of qn - 1. Our definition of f*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 f*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 - 2017

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Cyclotomic Polynomials
Divisor
Linear Group
Group Theory
Number theory
Finite Group
Subgroup
Family

Cite this

GLASBY, Stephen ; Lubeck, Frank ; Niemeyer, Alice ; Praeger, Cheryl. / Primitive prime divisors and the nTH cyclotomic polynomial. In: Journal of the Australian Mathematical Society. 2017 ; Vol. 102, No. 1. pp. 122-135.
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Primitive prime divisors and the nTH cyclotomic polynomial. / GLASBY, Stephen; Lubeck, Frank; Niemeyer, Alice; Praeger, Cheryl.

In: Journal of the Australian Mathematical Society, Vol. 102, No. 1, 2017, p. 122-135.

Research output: Contribution to journalArticle

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T1 - Primitive prime divisors and the nTH cyclotomic polynomial

AU - GLASBY, Stephen

AU - Lubeck, Frank

AU - Niemeyer, Alice

AU - Praeger, Cheryl

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