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Title: Primitive free elements of Galois fields
Author: Huczynska, Sophie
ISNI:       0000 0001 3583 4484
Awarding Body: University of Glasgow
Current Institution: University of Glasgow
Date of Award: 2002
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The key result linking the additive and multiplicative structure of a finite field is the Primitive Normal Basis Theorem; this was established by Lenstra and Schoof in 1987 in a proof which was heavily computational in nature. In this thesis, a new, theoretical proof of the theorem is given, and new estimates (in some cases, exact values) are given for the number of primitive free elements. A natural extension of the Primitive Normal Basis Theorem is to impose additional conditions on the primitive free elements; in particular, we may wish to specify the norm and trace of a primitive free element. The existence of at least one primitive free element of GF(qn) with specified norm and trace was established for n ³ 5 by Cohen in 2000; in this thesis, the result is proved for the most delicate cases, n = 4 and n = 3, thereby completing the general existence theorem.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics